What I mean is, how can people tell you're a Slovak unless you start speaking Slovak (which they might confuse for Czech) or something.
They ask me or I tell them what I am.
Why? Poles are Slavs. I'm a Polish-Canadian, ergo I'm a Slav. A Libyan is an Arab and a resident of Guangzhou is Chinese, even if their own ethnic group matters more to them.
I am a Slav, but you better don't call me a Slav because I am first and foremost a Slovak. I am a Slav, but you should never refer to me as such unless an appropriate situation comes up and you have my consent. Most Slavs will definitely find it insulting if you call them Slavs or god forbid try to compare them with other Slavs. Refer to them by their ethnicity and not some language group they have vague understanding of, a language group in which other ethnic groups are also counted and most likely ethnic groups they don't like. During WWII the Croats hated the Serbs so much that they, Croats, declared and taught in all schools and universities that Croats were not Slavs but Goths only so that they would not be placed in the same group as the Serbs.
This is similar to when you couldn't understand why Greeks don't see themselves as European and do not like being called Europeans by others. I repeat for the hundredth time: facts of reality are irrelevant. People will describe reality as it fits them. I remember once reading a good essay about Balkan peoples' perception of Westerners and it was that to them Westerners describe reality in an odd and different way, always using logic and trying to be rational, instead of being selective and accepting only what fits them.
They seem innocuous but they often hide some very malicious subtexts.
If you cannot tell an innocent joke from a malicious one then you lack experience with them. There is an appropriate situation and company for every jokes, you just need to learn when and how to tell them. Avoiding them completely is a bit dull in my opinion. I personal love jokes about Slovaks.