History is a part of its Culture
Since the breakup of Czechoslovakia into the Slovak Republic and the Czech Republic in 1993, Slovakia has existed as a separate state. It is also a "young nation," as it has spent the majority of its history as a component of other multinational governments like Austria-Hungary or Czechoslovakia. Consequently, certain persons could be sensitive to concerns relating to nationality.
When it comes to the Velvet divorce that divided Czechoslovakia, there is no animosity or bitterness, and the two countries continue to have excellent relations. You should be fine as long as you avoid referring to Slovakia as an element of another state. When speaking to nationalists, it is preferable to steer clear of the complicated subject of Slovakia's role during World War II. Similar to how the years of Communism had an impact on the nation, this can be a touchy subject.
Although Slovakia was once a part of the Soviet Union, neither the USSR nor the Russian Empire have ever been a part of it. Please keep this in mind. The relationship with the Roma/Gypsy minority is one of the more pressing topics, and people may have strong opinions on the matter. Never engage in a discussion about a topic unless you are well-versed in it.