You’ve got me beat: your list of likes is much more inclusive than mine.
Only toppings I like are:
Anchovies
Black olives
I will accept sausage to “go along to get along” if decorum warrants it.
Yep. Some of the best pizza I’ve had is wood (or coal) fired oven with a really good crust, a bit of sauce (or just olive oil) and a few pieces of fresh mozzarella.
95% of the time, I’ll get plain cheese pizza. If I’m sharing and I MUST have toppings, I generally only want garlic, and maybe mushrooms.
The only other topping I am into is one that’s seriously rare - shrimp.
I’ve had egg on pizza once or twice and it is indeed pretty good. The first time I ever tried it I was in Istanbul in a little café type place with a wood fired pizza oven. They put all the toppings on it and then just broke an egg on top of that in the middle and fired it up. It was outstanding.
There are only a few toppings that i ever prefer over a plain pie:
Ham/proscutto
Fresh mushrooms (not canned)
Artichoke hearts
Black olive
Rarely sausage
Ham & pineapple
And I once had a fabulous zucinni pizza, but I’ve had a few bad ones, and don’t order it.
None of those toppings should be excessive. None are required. But I do enjoy a little artichoke heart.
So when I eat with a group, I mostly eat plain pizza.
Grated carrots are even worse. It tasted like blasphemy.
Of standard pizza toppings, I don’t care for olives or anchovies or ham. Pepperoni is okay, but my favorite is a spicy red sauce, extra garlic, peppers, mushrooms and onion. If the pizza place offers artichokes, they are acceptable. I’ve had spectacularly good eggplant on pizza, but also horrendously awful eggplant. Plain cheese is good, too.
I’d go farther and recommend the pizza marinara at any place that does good Neapolitan style pies. Just tomatoes, garlic, oregano, and olive oil. No cheese. That and the pizza margherita are perhaps the most classic of Neapolitan pizzas.
Pizza means a lot of things to a lot of people, and I tend towards being a pizza inclusivist. But no cheese on a pizza is not a crazy idea–it’s completely normal in one of the holy cities of pizza - Napoli.
Funny, that is pretty much the top of my “won’t eat” list. 
Yeah, the OP has a pretty lengthy list of likes for saying he dislikes most toppings.
Left to my own devices, I’d generally order green pepper and onion. And I’m pretty easily satisfied by most veggie options (if there are enough veggies, the can even hide the olives! ;))
My wife prefers shrooms, so that is what we generally get.
If I’m PAYING for the za, or if we are only getting one pie, I’ll be more opinionated about what goes on it. But I’m pretty easy to go along with most groups.
Man, we haven’t ordered za for some time. Now you’ve got me thinking about it…!
I am so done with sausage and pepperoni. Sausage and pepperoni, over and over and over unto death. (and that goes for hot buffalo wings, too). I am a wife and mother who never in my whole life ever got to order what I want on a pizza, because they need sausage and pepperoni. The best I can do is beg for half the pizza to be plain cheese. (left to my own devices, I would choose green pepper, fresh mushrooms, a little anchovy, or a fancy-schmancy white clam-and-bacon or fresh mozzarella and basil leaf pizza from the expensive goor-may place.)
Anchovies in particular. If a pizza has black olives on it, I can pick enough of the damned things off that I can eat the rest of the pizza.
But if it has anchovies, I don’t even want to be in the same room with that pizza. Even removing the anchovies doesn’t fix it; the taste and smell of the anchovies were absorbed by the cheese.
But there are really only a few other pizza toppings that one sees fairly often that I won’t eat. I’ll eat a meat lover’s pizza, I’ll eat a veggie lover’s pizza, I’ll eat a plain cheese pizza, and pretty much anything in between those vertices.
As far as I’m concerned, pepperoni is too salty. I’ll take sausage, hamburger, Canadian bacon, Real Bacon (because bacon is good with everything) and even ham. Hell,if you want to throw a little chicken in there, sure. But no pepperoni.
And why would you clutter up a pizza with vegetables? That’s what salads are for!
I can’t think of any traditional American pizza topping that I wouldn’t happily eat.
I strongly prefer fresh Italian sausage but pepperoni is ok, too. Ground beef and chicken are too mild to stand up to rest of the pie and basically a waste of a topping. I’d still eat it, though. I’m ok with polarizing toppings like pineapple, anchovy, mushroom, olives, . Similarly, there are a few mentioned in this thread that I’ve never had before but wouldn’t hesitate to try like corn, peas, egg, shrimp, eggplant, tuna.
As far as non-traditional pizzas, I’m less enthusiastic. Barbecue pizza is ok in theory but the sauce is too sweet after a few bites. One 2x3 inch square is just enough. Chicken ranch is meh, I’m not a huge fan of ranch and using it as pizza sauce is a big dose. I don’t think I’ve ever had buffalo chicken pizza but I feel like I’d be sitting there wishing I had regular sausage pizza and a half dozen wings instead. White clam pizza sounds good, though.
WRT non-traditional pizzas, I still miss Truby’s Thai pizza, and its Greek pizza and Jamaican jerk pizza were damned good too. Truby’s (of Whitefish, MT) was the one pizzeria I’d been to that could do genuinely different pizzas like that, and do them so well that I’m still disappointed that there don’t seem to be any East Coast pizzerias that can do that sort of thing.
Of course, as a Firesign Theatre fan, this makes me think of Nick Danger: “No anchovies? You’ve got the wrong man. I spell my name - DANGER!”
Pizza Margherita was made to resemble the colors of the Italian flag. If two hundred years later you somehow think that is the pinnacle of culinary achievement you’re sorely mistaken.
Macaroni and cheese pizza is surprisingly good.
I will eat it with Funyuns while reading James Joyce
I like pepperoni too but it’s become difficult to find any that doesn’t have chicken or turkey in it. Last I checked, Dominos pepperoni does not have any poultry so that’s the only place I order pizza with pepperoni from. Other big chains (last I checked) do use it. Bleccch!
A Margherita pizza has at least two merits:
[ol]
[li]It’s a satisfying but simple pizza without all sorts of warring topping flavors. Almost refreshing. I usually order it when I want a pizza, but don’t have any particular cravings beyond that.[/li]
[li]It’s a great order the first time you visit a restaurant. The best way to judge the general quality of the pizzas being proffered. No distracting gimmicks, yet you can make a fair apples-to-apples comparison between establishments.[/li][/ol]
I’m that way with cashews, which for some odd reason are an ingredient in any number of pizzas in these parts. Can’t stand them, and they contaminate everything they touch. Anchovies, OTOH, are delish. But the best topping is none. Gimme a basic cheese New York slice and I’m happy.