This is the "world is going to end because we didn't plant grass today," argument. This fallacy often seems plausible. The slippery slope argument often hinges on worse and worse things until the world is basically ending. I most often see this when debating gay marriage and gender identity.
The argument with gay marriage is usually laid out as: if we have same sex marriage, what's next? Marriage between a man and his cow? Pedophiles marrying their victims? and so on and so forth. Generally speaking, this is absurd. The majority of people that say things like "people should be able to marry whomever they choose," are speaking of two consenting adults. Now, at the risk of falling prey to another logical fallacy, no, they don't always say it, but it is implied. "How is it implied?" you may ask. Well, I have never actually heard a logical, sane person argue for anything other than same sex marriage when they actually get into the argument. When pressed for more information on the policies they seek, they will argue for two consenting adults be allowed to marry regardless of gender.
The other way I see this fallacy is when people are discussing gender identity or sexual orientation. People will suddenly break in with something like "if I feel like a dog, that doesn't mean I am actually a dog." or "What next? people identifying as poodles." This is a bit extreme. From what I can tell, there are two basic genders, on either end of the spectrum. None of them come up with a whole new gender. There's male, female, gender fluid (both), and agendered (neither) for the main categories, and it may be somewhere in between for some. None of these are listed as poodle, duck, tree, or anything else. It's an extreme reaction to something the person doesn't understand.
This is the slippery slope. Neither of these things are really going to happen. We can even create laws to prevent them. The laws could state that marriage between consenting adults is legal, as long as all parties agree to the terms. It becomes less sexy then, but the government isn't very sexy to begin with. We also must acknowledge that separation of church and state means that there is no religious connotation of marriage under the legal definition. Churches may elect not to perform ceremonies, but they can for heterosexual couples as well. As far as gender, we can also limit this to only human genders. We can insist that people will choose a human gender. We don't have to acknowledge the ones who want to identify as a tree. Bathrooms should all be single stall unisex anyway, so don't get me started.
Don't fall down the slippery slope. Things that you do not approve of or understand may exist without the drama of thinking the worst will happen.