Unrelated to what "side" of the "war" people making statements are on, I would think that the typical role of the HR department would be to examine the context

Unrelated to what "side" of the "war" people making statements are on, I would think that the typical role of the HR department would be to examine the context surrounding inappropriate statements at work before taking action. If the HR department doesn't operate that way, or the company guidelines suggest that some statements demand reprimand regardless of context, then I would suggest the issue would be surrounding the way the HR department operates rather than the people making complaints to HR.