I completely reject slippery-slope arguments. For one thing, by this kind of logic, we should never change anything at all, since any change, no matter how obviously beneficial, can be portrayed as a potential gateway to some other hypothetical change that everyone agrees would be bad. Equally important, the historical record doesn't support the validity of such arguments.
One can imagine similar slippery-slope objections being made during controversies in the past --in the 1860s, "If we emancipate black slaves, it will lead to demands that horses be similarly emancipated from human ownership", or somewhat later, "If we allow blacks to vote, it will lead to demands that women be allowed to vote". For all I know, people might actually have made those precise objections at those times. They would have seemed just as logical then as slippery-slope objections to gay marriage do today, and they illustrate why such objections aren't valid.
To take the first example, as we now know (and as even quite a few people in the 19th century recognized), skin color is a superficial trait which doesn't inherently correlate with any human ability relevant to a capacity for citizenship or self-determination. The apparent differences in ability between the black and white populations in the US in the 1860s stemmed from the dramatically different levels of education, access to resources, and other environmental factors under which those populations had developed. Horses, by contrast, are an entirely different species, and no set of environmental conditions would allow a horse to develop the same mental abilities as a human. If there had ever been a serious movement to promote horses to full citizenship, it would easily have been exposed as absurd on its own merits, even among people who accepted that discrimination among humans on the basis of skin color was wrong.
As for the second example, as we all know, in the early 20th century there was indeed a movement to extend the vote to women, and it succeeded. Again, though, the question was settled on its own merits, not by mindless replication of the result of an earlier controversy. The case that women are as innately qualified for full citizenship as men are won the day, not just because a similar argument about race had been accepted earlier, but because it was valid on its own merits -- as the same case made for horses clearly would not be.
This does not mean, of course, that analogies between different social changes are never valid. I have myself sometimes compared the opponents of gay marriage with the opponents of interracial marriage a couple of generations ago. Advocates of, say, polygamy would no doubt offer similar analogies. But again, in each case, the analogy must stand or fall on its own merits -- are the opponents indeed motivated by mindless prejudice and visceral repulsion, or do they have a valid case in the present debate which opponents in the earlier debate did not?
My point is, even if proposed change X is accepted, that does not make the slippery slope to hypothetical change Y inevitable, though it may make the question easier to raise. Once gay marriage is legal nationwide and generally accepted (as seems inevitable now), we may indeed see serious efforts to win acceptance for polygamy, or brother-sister marriage, or human-animal marriage. But if so, the outcome of the ensuing debate over those proposals will not be a foregone conclusion just because gay marriage won out in its time. Each one will be debated on its own merits and will be accepted or rejected on its own merits.