In my experience, the best response is one in which you make it clear that you personally care about the customer's problem and will do your best to get it resolved quickly. This trumps everything else, so long as it's the truth. If your engineers don't actually care about your customers' problems, then having them do support will only hurt your business.

If it comes down to that, yes. Though I'd first try to track down their requests in the logs and see if it's something we can fix on our end.

Obviously, some companies make a conscious decision not to support all browsers, so there might be no way around it in that case.

So you would, eventually, get around to asking the user to use another browser? Just not as abruptly?