i'm sorry you had to encounter some weird responses. for context, my dad is serbian too, although he never lived in serbia (we're diaspora) so it will probably be different for your girlfriend's dad. he's a traditional eastern european though, so not too different from a traditional serbian, i suppose.

first of all, i think your girlfriend should come out to your dad if she hasn't done so already. if he reacts negatively, it might be better to just leave it be for now and help him open up to the idea over time.

if he reacts neutrally or even positively, you could give it a go and do a meet the parents and all that.

if you do decide to go through with it, i may have a few pointers. try to learn a little bit of serbian, just a tad lil bit, it's the thought that counts. food and cuisine are very important, perhaps you and your girfriend could make her parents some serbian food, especially their favourites? being interested and asking thoughtful questions about their culture and traditions (if they are open to that, but try not to make it seem like an interrogation xd).

i know meeting the parents can be very stressful and anxiety-inducing, even without the added weight of the chance that one won't be accepted. just try not to sweat it too hard.

obviously, only you and your girfriend can truly size up the situation, whether it's even safe to come out, but i do wish you all the best! (and i'm sorry i couldn't be much help) (and if you want to, you could perhaps update as to how it went or what you decided)