Yes, awareness of the situation is wise and a part of basic decency. If this guy was being loudly offensive like the restaurant's statement said, I can see a good case to kick him out.
On the other hand, kicking someone out solely based on politics even if they're not loud is a different story. I feel unsafe and avoid even quiet conversation about certain topics in public because the reception of my views where I live could compromise my physical safety.
I'm not sure what he actually said or how loud he might have said it. This is where video footage might have come in handy, but I can understand where some people might get a bit loud in restaurants, especially if it's crowded and a lot of people are talking. Sometimes voices carry and one can unintentionally eavesdrop on someone else's conversation.
I've noticed it to be more of a regional thing, at least in America. I see that this occurred in Miami, so maybe it was in a more liberal area. If he had been up in northern Florida or somewhere around Mar-A-Lago, they might have given him a free Grand Slam breakfast. That's where liberals might be harassed and kicked out of places.
Actually, when it comes to canceling, harassing, and kicking people out of places, conservatives actually do have a far worse track record in that regard, at least historically in the American experience. (Actually, even much worse than that.) So, when put against that historical perspective, it might seem to some to be some petty, feeble complaint from a conservative about being kicked out of a liberal place because of his politics. Not that I'm saying that's what happened (since it's not really clear), but I can see where some people might find it hard to be sympathetic under the circumstances.
If that's what it is, then I probably wouldn't have a great problem with it. My only real issue is when a statement or idea which might be mildly politically incorrect is lumped in with the worst of the worst. It creates a false perception in society which leads to confusion and an inability to properly differentiate between what is truly dangerous versus what may be relatively more innocuous. That seems to be a growing complaint these days, that a disturbingly growing number of people aren't able to distinguish what is true and what is false.