While it's true that language is often not the problem, it's less relevant to the discussion of what words to use as a caller than you might think.
Scenario A:
If we have to keep finding new ways to describe square dancing because it's viewed as an activity only danced by weird old white people, then square dancing is the problem and changing the name isn't going to help.
Scenario B:
If the problem is that an activity like square dancing has borrowed terminology that has become dated over time, then it can avoid becoming scenario A by updating its terminology to match the moving target of society or in some cases it can discard that terminology in favor of something that is less likely to attract baggage.
As regards the original question for this post, how we refer to people is going to be a moving target. If you want to avoid offending people, you should probably find a term that is considered respectful in the current era in which you are living. If you don't care about offending people, then the question is moot.
As regards other terminology concerns, if you find that you have a dance term that refers to specific people or groups (gypsies, contras, etc.) you can, in fact, avoid the problem (possibly forever) by moving the term to something less likely to get wrapped up in the identities of groups or cultures.