Here in 'Murica, most people are quite offended by the "N-word". Of course, insulting someone personally would be more offensive than the good ol' "N-word", but as a general insult/offensive word, this would probably be the worst.
General advice. If you are discussing the nature of insults you can use the word that is insulting in the discussion. If you censor said word, other than as a workaround for autocorrect or something, it reflects poorly. A word may well cause problems in many contexts but it should never be in an academic discussion of the word, or when you are clearly not espousing the views that led to the word becoming a troubling word. That said I plan to continue feigning ignorance about the American dislike of the word cunt, mainly as it is hilarious.
Swearing is possibly my favourite part of linguistics and language comparison. Morphing of concepts as well is also good -- racial epithets now tend to reflect more poorly on the one using it (UK wise n**** is not a great word to be using, and the UK also had paki, normally aimed at those of Asian*, which could take a while to unpack), as do many of those dealing with disability (though retard is still fair game at lot of the time). It remains to be seen whether those of gender (don't be a fucking girl) or financial wellbeing face similar fates, though finance is probably going to be rooted more in class (see also the politician that got in trouble around the word pleb, and because everything has gate attached to it then it was called plebgate). Religion still peppers the more extreme end of language (fucking/bloody hell** and Jesus [fucking/cocksucking/cunting/... Christ] are you planning to eat the whole thing) but among the general populace there are no insults based on it any more. I am sure if you are one of the few that actively pursues religion, or are otherwise in one and speaking to others in it or competing ones then there may be something.
Faggot would be understood but if you asked someone if they knew where they can find some fags you are more likely asking where a newsagents is as you want to buy some cigarettes. Likewise the phrase fucking fags is uttered more after someone is coughing up a lung.
I don't doubt transgender people face problems others might not, in addition to those that everybody faces, but as a general insult I am not sure there are any. Then again live and live let seems to be general policy here.
Cocksucker is probably a general insult for anybody now, though probably more males. Gay tends mainly to be used by 8 year olds, or in jest among close friends.
*Asian in the UK tends to mean Pakistan, India, Bangladesh type places. Oriental is used for China, Thailand, Vietnam, Japan.... and is absolutely not an insult or bad thing to call a person -- that oriental feller that lives down the road from you is absolutely fine to say, and should you walk up to his door and say "my mate says there is an oriental feller that lives down the road and he can fix my problem, is that you?" it would be fine too.
**tends to be with two l characters today, some have wondered whether is was the more the Norse folklore Hel being co-opted in various means (Christianity being quite good at that). Either way few would consider that today.
All that said the prevalence of US culture does seem to have allowed some things to creep in and morph some things.