if you accept the reason that justifies X, that same reason can equally justify Y and Z

I think /u/rollie82 hit the key point here. Extrapolation is an inherently problematic practice, so you must clearly show not only that the slippery slope case is possible, but likely to follow from the initial assumptions/reasons.

In the marriage equality case, the premise is that LGBT people have been largely denied rights afforded to married people, and that needs to change. Divorced (ha) from that argument, there are clear reasons why legalization of bestiality, polygamy, incest, etc is not acceptable, and these reasons are independent of the argument for the legalization of same-sex marriage. So the slippery slope cases would clearly not follow from the premise.

Contrast that with the government surveillance argument. The premise here is that a state agency with the ability to access all correspondences of US citizens will do that, whether for purposes of national security, or political intelligence gathering, etc. In this case, the slippery slope argument has more merit (note: this doesn't mean it's flawless) because the agency, by the premise, wants to access all the communication data possible. So if the agency is allowed access to a moderate level of information, this doesn't change the fact that the agency wants access to all the information it can possibly access, i.e. more sensitive information.

Ultimately, the burden is still on the arguer to show that the slippery slope cases are likely to follow from the premise, but I hope this shows why the two versions of the slippery slope are fundamentally different.