No true Scotsmanis a fallacy, more specifically ad hoc while defending a generalisation about a group defined by another criterion. Easier shown with an example:
[Alice] Vegetarians don’t eat cheese.
[Bob] I know plenty vegetarians who eat cheese. They just don’t eat meat.
[Alice] Those who eat cheese are not true vegetarians.
If we accept the definition of vegetarian that you implied (someone who doesn’t eat meat), “not eating cheese” is at most a generalisation. As such, when Alice says “Those who eat cheese are not true vegetarians”, she is incurring in the fallacy.
The slippery slope is an interesting case, because it’s both a fallacy and a social phenomenon. And evoking the social phenomenon doesn’t automatically mean that you’re using the fallacy.
As a fallacy, it’s failure to acknowledge that the confidence in the conclusion is smaller than the confidence in the premises - so if you’re chaining lots of premises, your trust in the conclusion will degrade to nothing. Here’s a simple example of that:
if A happens, then B will happen 90% of the time. if A doesn’t happen, B never happens.
if B happens, then C will happen 90% of the time. if B doesn’t happen, C never happens.
[…C then D, D then E, E then F, in the same fashion as above]
if F happens, then G will happen 90% of the time. if F doesn’t happen, G never happens.
So if A happens, what’s the likelihood of G also happening? It is not 90%, but (90%)⁶ = 53%. Even with rather good confidence in the premises, the conclusion is a coin flip. (Incidentally, a similar reasoning can be used to back up Ockham’s Razor.)
As a social phenomenon, however, the slippery slope is simply an observed pattern: if a group, entity or individual does something, it’s/they’re likely to do something similar but not necessarily identical in the future. That covers your example with fascists.
The same sort of thing happens all the time with ‘Appeal to Authority’, you can probably trust a scientific consensus about a subject in which they are all experts, but you probably shouldn’t trust an individual expert on a topic for which they are not recognized as an expert.
The reason why appeal to authority is a fallacy (more specifically, a genetic fallacy) is because the truth value of a proposition does not depend on who proposes it. If an expert said that 2+2=5 (NB: natural numbers), it would be still false; and if the village idiot said that 2+2=4, it would be still true.
We can still use authority however, but that requires inductive reasoning (like the one I did for the slippery slope), that is considerably weaker than deductive reasoning. And it can be still contradicted if you manage to back up an opposing claim with either 1) deductive logic, or 2) inductive logic with more trustable premises.