First, the answer to all your hypotheticals is "yes". Second, and this is what is a little misleading about this particular case, the Christian group didn't really receive public "funding". They were, like any recognized group on campus, assigned a building and room in which to meet. That, say the justices, constitutes "public funding"; access to public property.
I haven't read the decision in it's entirety yet (I'm barely a 1/4 of the way through MacDonald), but I'm interested especially in Alito's lengthy dissent. I'm worried what this might do to the Boy Scouts of America, who receive no public funding but are allowed to use public property.
Yes, that is the crux of the matter.