my console inboxes are full of messages ... just for beating people in an online game or not playing in a way they approve of. And no one comes to my rescue at all.

Well, other players in-game aren't exactly privy to your inbox. So I'm assuming you also receive harassment over voice chat in-game, for which others could potentially call out the harassers for being jerks.

Also curious, what games are you playing that other people would take the time to actually write a threatening message to your gamertag/PSN ID after losing a match to you? (I honestly have no idea how common this is, as I rarely play online multiplayer on console. Just seems like an awful lot of effort for someone to do that on console.)

When you find a way to resolve the issue, let us know - I guarantee more straight white males will be relieved than anyone else...

Well sure, they're probably the majority of players in online multiplayer games. So by pure numbers, maybe more of them receive harassment. I'm guessing a larger percentage of women (who use mics) receive targeted harassment like OP describes.

But yes, it's a problem that affects many people, and harassment and threats are never acceptable.