You would start talking to him if you feel comfortable doing so. And/or send a letter to the bishop, if in fact the novel ideas are in conflict with the teaching and guidelines of the church.
He seems to be a universalist, but I haven’t heard anything explicitly heretical.
On the possible solutions…
go to a different parish: I’ve been going to this parish for over a decade, and I have many friends here; I’m unwilling to leave.
withhold funds: I hate the idea of hurting the people who get financial help from the parish.
ask the bishop to remove him: I’m reluctant to ask for another priest when they’re so scarce.
I’ll ask you what I asked the bishop - how do I support the pastor without supporting his questionable ideas? (And I hope to get something better than, like, “thanks for bringing this up, we’ll talk to him, pray about it.”)
PS. Yes, there are a lot of truthseekers, but I like being inconspicuous.
Does your parish have a lay council? I believe they’re supposed to handle the business affairs of the parish so the priest’s time can be freed up (or possibly split among other parishes.) If you talk to the parish council, you may get a better hearing for your objections, and they’ll have more clout when talking to the priest.
For that matter, has anyone talked to the priest about it? He may not like criticism, but he won’t excommunicate you.
Well, you’re missing the obvious course of action, which is “talk to the pastor”.
Possibly he doesn’t appreciate how what he says comes across to you, or how it affects you. Possibly you’re misunderstanding what he says. Possibly he’d be genuinely upset at the thought that he’s upsetting you and others, and would be anxious to avoid that. There’s all kinds of ways that this issue could be addressed by two adults committed to a shared faith who are willing to talk to one another and listen to one another.
This should be the first avenue which occurs to you and, if it isn’t, that suggests that you’re in a dysfunctional parish or that your relationship with your parish is somewhat dysfunctional. And in either of those cases you have a problem which has nothing to do with the pastor’s theological views.
Do this during communion.
Well, as someone said above, you can always vote with your feet.
I am not Catholic (well, not large-C Catholic), but I have been associated with a specific church for over 30 years now, which encompasses five rectors. Every new tenure sees some shifting of people. Some folks just see a change in priest as an opportunity to go try somewhere new (or just stay home). Others had a particular negative reaction to the newcomer or the one who just left. In one case a couple felt that the priest had given an anti-military sermon and they had a son in the Navy and were not pleased. They had been very involved and then they stopped coming altogether. The moment the next priest was appointed they were back again and very involved. (New Priest was no different in his view of the military than Old Priest, in my estimation, but not in theirs.)
On a broader level, my (large-C) Catholic uncle and aunt stopped going to their church when Pope Benedict ascended to power. Pope Nazi, they called him, both for his past and for some of his attitudes and actions as pope. They were not much enamored of their local priest at the time either, but were focused much more on the change in pope.
You can also decide you’d prefer to stick with it regardless of your problems with the priest. Especially if the congregation as a whole is important to you. That’s legitimate too. We had one priest a while back that I just never clicked with–I never quite understood where he was coming from on a bunch of things–but we kept going because it was “our” church and we had friends there and the kids were reasonably happy with it, and because we knew he’d eventually leave and someone else would come in. (Which happened, and we liked that replacement a lot better.)
But as UDS says, bringing your concerns to the priest himself, trying to find out what the guy thinks (and what he thinks he’s doing), is a good first step, and one that I think a lot of disgruntled parishioners avoid. I don’t *know *that you’ll get anywhere. You may not. Some clergy really don’t like to be challenged, and my (anecdotal) sense is that for a bunch of reasons this is more of an issue in the RC church than in, say, mainline liberal Protestantism. The priest may get defensive or simply refuse to engage in discussion about these things with a lay person. Hierarchy and all, I’m the expert and you’re not. My way or the highway; I’m in charge here. But you won’t know unless you try.
I fail to see how something that’s so common it doesn’t even come up can be harder than something that while common does draw attention. Did we just stumble into yet another of those things where Protestant notions of Catholicism are very different from Catholic notions of Catholicism?
Same thing you do if you don’t like the food at a restaurant, you stop going.
Just wait until the right people are in the room then ask the air if no one will rid you of the turbulent fellow.
Ask very loudly for someone to rid you of the troublesome priest. I heard that worked before.
Make a pact with Satan for a different priest.
There are many, of the last mentioned (and in the US at least firmly anti-religious people tend to be Protestant by background, or anyway make Protestant assumptions about Christianity, it’s basically a Protestant country originally). Anyway in reality in US Catholicism as I know it, it’s very unlikely there would be any intersection practically speaking of worshipers and clergy knowing/caring that the parishioner could be going to a closer church. ‘Oh you come here but you live there, you should really be going to St X’. That conversation is not going to happen in reality.
And years ago obviously not, as in the origin of 4 churches within around 10 minutes walk of our house. Ours was the Irish one, another the German, the two others Italian with connection to different places in Italy (established as the immigrant community evolved ca. 1850’s-1920’s). That’s no longer particularly true in this town, but back in the day obviously the Church felt that was fine. In the next city over there’s a Polish and an Italian church on the same block, which retain their ethnic origins.
Also often ‘church shopping’ Protestants are shopping denominations, and/or independent churches. With Catholicism it would be more like a Walmart or McD farther from your house asking why you don’t go to the closer one. 
Another thought, and perhaps one the OP would rather not hear:
In an episcopal (bishop-based) church such as the Roman Catholic Church, priests who lead parishes are in some sense proxies for the bishop. I am not quite sure how the assigning-of-priests-to-parishes works throughout the church, but in the RC cases I’m most familiar with, the bishop essentially assigns the parish a priest. Obviously there are considerations such as who REALLY needs a new parish home, which priests have been moved quite recently, whether there are enough priests to go around, etc., but ideally when a vacancy is available the bishop tries to figure out which priest will be a good “fit” with the parish. That’s a decision that might involve ethnicity, or economic background, or a host of other things.
Thus, it may make sense to assume that the bishop WANTS this particular priest in the OP’s parish. And it doesn’t strain the bounds of credulity to imagine that the bishop sent Priest X to the OP’s congregation to shake things up a bit–to argue for some new ideas, some new ways of thinking about the church and what it stands for. In this case the bishop is not going to be very responsive to an appeal to move the damn priest already–he had a good reason to put the guy there to begin with.
As mentioned before, I am not RC but I do belong to another denomination with bishops, and have served on two search committees to find new rectors, so I am will acquainted with our diocese’s process. The bishop is involved in the process and has a degree of veto power, and thus it is not entirely up to the parish. The last thing a bishop wants is to have a parish saddled with a priest they don’t like, so usually there’s pretty good vetting at the top. If anything, I’d expect more of this from the generally more centralized and hierarchical RC church. Thus, while it’s possible the OP’s bishop has no idea what a fine mess the new priest is making of the OP’s church, I would not be quick to assume that the bishop disapproves or that the priest’s new ideas don’t have the bishop’s backing.
It’s not really a “should”, but people have idly said, “Oh, you don’t go to <parish I am in the region of>?”
I agree if it is a matter of the style of the priest, etc. I still believe the bishop would want to know if the priest is expressing something contrary to the Church.
In the Roman Catholic church of 50-60 years ago, it was common for a priest to stay at one parish for years & years. Starting as the assistant, then becoming pastor when the old priest died/retired, and staying pastor there until he decided to retire. A common sentiment was that when a priest began marrying people whom he remembered baptizing (or baptizing their parents), it was time for him to semi-retire by moving to a smaller parish. (That was back when the Church had lots of priests available.)
Now, it’s much more common for bishops to move priests every 7-10 years. {A cynical comment on that practice was that 7 years was the statute-of-limitation period in most states. But that’s mostly been changed now, and Civil lawsuits are the big worry anyway.]
Bishops assign priests to specific parishes for various reasons.
Often they try to somewhat match the priest to the parish: send the young, liberal priest to a liberal parish, where he’ll fit in; rather than the old hide-bound conservative parish that wouldn’t like him. But sometimes the bishop sends a priest there to ‘change’ a parish. Some of the Pope Benedict bishops sent conservative priests to ‘liberal’ parishes, with the intent that they would ‘rein in’ this parish. That didn’t always work well.
I like to think before I speak. I realize that’s more peculiar than ever nowadays, but I hope you (plural) will have some patience with me.
And in defense of the bishop (whom I criticized for sending me a form letter), bishops probably get a lot of letters like* “Father OldGuy always used to do X, but now Father NewGuy is doing Y. The Vandals are at the gate!!”
- except in Latin
If you like your priest, you can keep your priest. Otherwise, the only choice you have is to switch churches.
Yes, this. My husband started going to another nearby parish. It wasn’t necessarily because of the priest though, he just enjoys it more, I think he gets more out of it. I don’t attend so, I don’t know, I haven’t gotten anything remotely spiritual from it in ages. I need to read the rest of this thread, I’m curious what the priest is doing that’s rubbing a lot of the parishioners the wrong way.
Made my day 
I was raised Catholic, years of Catholic school, but could someone explain to me what the OP means when he says the priest is a universalist? Doesn’t Catholic mean universal? I really have no clue. Is the priest from some university? Color me naive.