The problem I have with the article (and the topic) is that we are not told what "“the language they were using [that] was unwelcome in our space” actually was. Were they espousing conservative ideas like smaller government, or respect for traditions and not tearing down statues? Or were they discussing things like who should be barred from getting married, and who ought to be strung up as "woke?" Tell me something about that, and I'd be better able to answer.
In my view, any speech which does not threaten harm or hate to others ought to be tolerated by anyone. I'm basically liberal in my politics, but would never think to try to silence someone expressing a conservative economic viewpoint. However, I might think differently about discussing conservative "social values" in a public space that very likely has room for people who are being referred to. Gays and transexuals do eat in restaurants, after all.
I think that's the point I would make, too. There's genuine, overt hate speech which is obvious and plain to anyone who can see it, but then there's other situations where it might not be so obvious or overt, yet some people might still react to it and treat it as the same.