Almost everyone who uses social media regularly has had threats from some or other wingnut. I got some little 4Chan tosspot send an ART after me a few years ago which, due to circumstances, was more comedy gold than a distressing experience. I considered it somewhat unsporting, too, as whoever it was didn’t even bother calling me a fat ugly lesbian manhater first.
Threats can be terrifying, even if they are more hot air than real danger, of course: another individual took to plaguing me with insults and one or two statements that I was going to be duffed up at some point – even though I never feared physical harm from this person (because I knew who it was, and reckoned that I could probably just push them over with one finger if they were to show up on the doorstep), I didn’t sleep well, and found I couldn’t switch the computer on without spells of shuddering and nausea, while it was ongoing.
But there are threats, and there are threats. One group of wingnuts very fond of claiming to be ‘threatened’ all the time are, of course, the GC crybullies. These are the people who have to make everything about them and the Terrible Trans Menace; the ones who are claiming that a recent threat received by JK Rowling is the fault of trans people when it is surely blindingly obvious that the person who sent her the unpleasant threat did so because she (rightly) spoke 
out in sympathy and solidarity with Salman Rushdie: the person who made the threat appears to be an Islamic fundamentalist rather than some angry trans teenager. The only other actual threats directed at anti-trans posters (the same two or three endlessly reposted by GC crybullies) seem to be the work of young cishet male ‘shitposting edgelords’ with no real intent behind them.
There is also a tendency among crybully types to confuse insults such as ‘Fuck you and everything about you’ and even straightforward disagreement or criticism with credible threats of harm. However annoying, spiteful and blatantly wrong someone is, threatening them with violence or murder is not acceptable, ever. But wailing and attention-seeking because you’ve been criticised for expressing your (ignorant and bigoted and, most importantly, downward-punching) views at a time when someone else has suffered an actual attempt to kill them for a book they wrote… that’s not great. Nor is insisting that someone is on the side of threat-wielders because they won’t defend you against insults and disagreements, especially when your motivation is to stir up more hatred against an already-demonized community.