fwiw, "no true scotsman" is generally not an actual fallacy, in terms of meaningful logical analysis. it's a fake fallacy, pushed mostly by english majors; logicians aren't going to get upset about arguments of this sort, with caveats for extreme cases.

and, usually, it's the person accusing you of the fallacy that is actually committing an actual error in logic.

ideas have definitions, and there's nothing inconsistent or illogical about insisting that you hold to the core concepts of an ideology if you're going to promote yourself as adhering to it.

regarding scotsmen, you'd have to define what it means to be one, first. if you decided that a scotsman has to be a certain amount scottish, then it's not in any wrong to deny the scottishness of somebody that doesn't fit your definition, as you presented it. we can argue about the definition, and whether our arguments follow from the definition using the proper rules of propositional calculus (if we agree on that system), but we can't have a meaningful debate about an actual assumption. what english majors will generally suggest is that the definition is arbitrary, and the value of their argument may depend on context, but that's not an error in logic; it's not a fallacy, of any sort, and using these arguments is not actually wrong in any way.

with socialism, it's at least supposed to have a meaning about worker control of production, and it's supposed to come out of the writings of karl marx. while this opens a lot of space for dissent, there are certain key components of the system that champagne socialists just can't actually make actual sense of.

so, if your concern is logic and consistency, there's nothing wrong with telling them they aren't socialists; in many cases, there is something wrong with letting a person perpetuate a system that has nothing to do with the words they're using to describe it.