Damnit, I came so close to the end of the thread before finding that somebody had already used my awesome answer!
But yeah, that.
OK, we send two people back through the time portal!
Was I born in this time or did I travel back? Do I have all my memories that I have now?
I, me, would support gay marriage in 1916, presidential candidate or not.
edit: for brevity.
Did the concept of homosexuality as what you were rather than something you did even exist in 1916?
I hope I would have been a member of the IWW in 1916 and thus opposed to capitalism and the state and so not interested in running for president. As an immigrant, transient worker, I wouldn’t even have a vote. Since I would have attended Emma Goldman’s lectures when I wasn’t organizing a strike, getting hosed in a free speech fight, or trying to get Joe Hill freed, I would been sympathetic and supportive of homosexuality and free love.
Democratic support for gay marriage at that time would have thrown the White House into the hands of the Republican Party until 1932, at least!
Well, if that’s the question, I can say that I have supported gay marriage since I was old enough to understand the concept, which was in the mid-70s. At that time, SSM was a highly unpopular (IIRC, about 30% support) idea, but not completely unheard of as it was in 1916.
The question as posed simply can’t be taken seriously. If I had been born a century ago, I would have been raised in a completely different cultural and intellectual environment and no doubt would have held very different positions than I actually do on pretty much every issue imaginable.
Or if we’re positing a time travel scenario: Of all the things I might consider doing if I had a time machine, running for President in 1916 wouldn’t come anywhere near making the list, so I can’t speak for what some hypothetical “me” who did want to do that might have done.
If, for some reason, time-traveling me considered it essential to get elected President in 1916, obviously I wouldn’t campaign on that issue, because it would have been political suicide.
If we take out the running for President angle and I happened to be transported to 1916, sure, I would advocate for radically progressive positions on this and any number of issues, but I certainly wouldn’t try to get elected to public office based on such positions, because there would have been no realistic chance of doing so.
I’d support SSM in 2016 but I wouldn’t in 1916 because it’d be a total vote loser. If I’m in, then I’m in to win.
Great answer 
John Mace just copied my answer from post #5. 
By this “whatever-wins-elections” logic, if slavery of black people were a vote winner in 1836, and abolition of slavery a vote loser in 1836, would you support slavery in 1836?
Not that I’m comparing non-recognition of SSM to slavery, but you get my point.
“Homosexual,” meaning, “An innate and unchangeable preference for sexual and romantic relationships with people of your own gender,” was first coined in 1869 by Karl-Maria Kertbeny, although, of course, in 1916, his ideas were still not terribly wide-spread or well accepted. But the idea was out there, and gaining a lot of currency even that early on.
Okay, I stand corrected on interracial marriage laws.
Dunno about gay marriage, but I would have spoken out publicly against this.
Would you?
In a silly hypothetical where you are transported back to 1836 and put into a position to be a viable candidate to run for president and shape the future of the country, would you take an anti-slavery stance or would you pull out all the stops in an attempt to secure the election?
I’m now imagining all of the 2016 candidates thinking, I dunno, pleasepleaseplease don’t ask me about polygamy, because if I’m asked then I’ll totally have to admit that I support it, but I can keep my mouth shut as long as it doesn’t come up…
I am, above all else, pragmatic. Advocating the legalization of gay marriage would at best have drawn a collective “huh?” and at worst would have led to “burn the heretic!” Anyway, almost nobody was openly gay in 1916 and so there was hardly anyone who would have wanted to get married. It would have been career suicide for most gays, not to mention actual suicide in many cases.
So, no. But I sure as hell would today.
Reading the question in the OP literally in terms of how it would be viewed at the time, I would very definitely come out in favor of gay marriage as a candidate, and would be surprised if anyone at the time opposed me on the issue. I think if you asked any man on the street whether marriages should ideally be gay he would answer in the affirmative. They should be light hearted and care free. But this of course has nothing to do with homo-erotic marriage which is a whole different kettle of fish. Supporting the later would have me labeled as a dangerous, radical, libertine, anarchist, and remove any chance I would have of pushing any reform in areas such as racism and role of the US into the great war where I might conceivably have influence.
Heck as late as the mid 90’s I wasn’t sure that pursuing same sex marriage was the right strategy for the gay rights movement as I thought it might be moving too fast too soon. Far better I thought would be to simply work towards anti-discrimination.
The attitude of many posters seems to be, “What ultimately matters in a political issue is what stance will get me votes.”
When you are the one running for office, not just a voter, that is a major concern. That is, unless you are running just to make a statement and not because you want to win. I can understand not wanting to put in all of the effort a presidential campaign entails unless there was a real chance of becoming president.