Does the "N-word privilege" apply to homosexuals as well?
Absolutely! The privilege has always been about the degree to which offense could reasonably be taken from your use of the word, not the particulars of the word. Cultural norms make it fairly reasonable to infer that using "faggot" indicates disregard for or outright antipathy toward gay folks, just as using "nigger" indicates the same for black ones. Context, of course, is everything, and one of the strongest contextual signals you can pick up on is the identity of the speaker - it's a lot less immediately clear that a member of the group in question would feel that way toward themselves. Of course, there are other cues that can indicate the same lack of negligence or malice. I hope this conversation is one of them, or else I'll feel mighty guilty for using the words myself just now!
Now, you might be thinking, "You say 'negligence' like it's just as bad, but I can't possibly be aware of every possible reason every possible listener could have for taking offense!" And that's certainly true, you can't - and shouldn't be expected to. This is where apologies come in - if you use the word in a context where somebody does take offense, then you fucked up. It doesn't mean you're a terrible person, but it does generally merit an apology, in the same way as if you bumped into somebody on the sidewalk. Apologize sincerely, move on, and let the other person handle it how they will. If they refuse the apology, that's their business, but they shouldn't be surprised if you don't see a need to do much more than that. And, of course, if someone takes offense on behalf of somebody who's not even present, they may or may not be acting a bit silly, so use your judgment as to whether or not an apology is merited or whether they're just being a dick. Social cues should be considered here, too - it may be that you feel you're morally in the wrong, but you might lose social face for sticking up for yourself, so it's worth considering whether that's a price you're willing to pay.
Finally, bear in mind that learning is a thing. If you repeatedly make the same mistake, it might be worth altering your long-term behavior instead of just watching your tongue for the rest of the conversation. So, while you shouldn't be expected to realize that "faggot" is a word you should use carefully right off the bat, if people keep objecting you should probably realize that your social circles don't like you using it, and adjust your behavior accordingly, just as you might do to avoid swearing at church, or whatever analogy floats your goat.