I think if someone's fault it "purveyor of hate speech," it's okay to point as much out.
Would this be one of those times when it's appropriate to get a bewildered look on your face, blink a few times in confusion and then say, "Umm...do you realize you just said that out loud?" Subtle, yes, so they may not get it, but if it causes them to think about what they said, even for a second, then you've accomplished something with a minimal amount of confrontation.Like this very much and will use. Very nice.
I wouldn't, unless you want a confrontation. It's not subtle and is widely accepted as a way of pointing out someone's faults.
True, but it's not likely to be taken well, so you're still likely to get the confrontation. If you know you're likely to provoke a hostile response and you're okay with that, by all means.