Well, first off, one thing you ought to keep in mind is that the modern day stupid discriminatory bullshit is really no different than what has existed since forever. If anything society has progressed to be better than it once was. There used to be more things that were widely accepted as reasons to hate a person or group of people, such as how even fairly progressive folks back in the day used to look at people with brown skin as second-class citizens; the non-progressive ones viewed them as subhuman animals, for comparison. It used to be the case that women were quite literally property in the vast majority if countries. Homosexuality used to be seen as a sign of evil wrongness by the vast majority of people in every country.
Shit still sucks, but it
has improved. Women are no longer seen as property in most places. While racial discrimination may exist everywhere, most places don't actually openly declare that people of different skin colors are lesser beings, and lots of places have special laws to make racially motivated crimes even more punishing than a regular crime of the same kind, which is a clear statement against racism. Homosexuality is still a pretty touchy issue because the main body of the movement to fight ignorance about it started quite a bit later than the other two topics, but now most western nations have done away with their archaic laws that make homosexuality and sodomy illegal, and a lot of them have fully recognized gay couples as having exactly the same legal status as heterosexual couples. Is society perfect in any of these regards? Fuck no. But it's moving in a positive direction, and that's something you ought to focus on if you want to try to move your focus away from what's wrong nowadays. Compare civil rights from 100 years ago to today and marvel at all that progress.
Now, for a couple of those things you've mentioned there hasn't been much forward movement on them. Gender identity is a rather new concept as far as public awareness goes, so of course there hasn't been much change in that regard. This stuff takes time. There's also the fact that it has latched onto the sexuality topic rather than being its own entity, so it's kind of tied to the sexuality acceptance discussion as a secondary issue, which means it's naturally lagging behind the slow progress being made on that front. Even so, there have been movements in the right direction, albeit small ones: lots of documents and forms for governments and companies give you a whole bevvy of options instead of just "male, female, or other," and some places have started either putting in special restrooms for non-binary gender people (which can be seen as a sort of "separate but equal" thing but is still a step up from total demonizing hate) or put rules in place saying that people can use whichever restroom fits their gender identity. Small steps, but steps nonetheless.
As for the mention of men killing women for not wanting to go out with them, eh, two things. First, there are women who kill men for similar reasons (less of them, certainly, but they still exist), which is very relevant to the other thing. Second, people will always rationalize reasons to kill people who annoy them. Some people are mentally ill and that screws with their judgment and they kill someone, then when they blame it on "but she wouldn't bang me" people latch onto that as the true explanation rather than the fact of their mental illness. You can see a prime example of this in the case of Elliot Rodger, the man who shot a bunch of people and then himself after posting videos talking about how it was wrong for women to not be with him. People focused on that aspect of it rather than the fact that not only was he clearly mentally unstable from those videos, but he had a long history of psychological problems. Basically what I'm saying here is that "she wouldn't date me" is probably never the actual core cause of a murder, it's just the trigger that happens to set off a dangerously unstable mind. Sane men by definition don't go off and murder women because they don't return their affection.
I won't bother with the religious bit much. I'm an agnostic atheist, so that should answer how I feel about the concept, haha.
Anyway, all that said, there are a few ways you could try to either stop worrying about this stuff or to worry about it less. The first, which I already mentioned, is to try to pay more attention to the progress that has been made than to the shitty circumstances that remain. For something easier to relate to than the 100 year thing I mentioned, go take a look at how things have changed in your lifetime. Tons of new laws and movements against discrimination of all kind have popped up in the past couple decades, definitely enough to show a marked increase in civil rights in that time. Being able to look at it and clearly see progress that has been made recently, then looking at all the groups and people that are still pushing forward today, might help.
Another thing that might help is getting out there and being part of that moving front of positive change. There's a lot to be said for feeling like you're part of the solution rather than sitting on the sidelines and being angry about it. Fuel all that anger about things into constructive action to try to change it. I would highly suggest you try to do this by way of actual real life efforts rather than internet efforts, since those aren't very useful and probably won't make you feel like you're actively helping a cause.
The third and final thing I can think of is probably the least healthy way to deal with it, and it also happens to be my preferred method because I'm a shit. Embrace the misanthropy and cultivate apathy through my Three R's Method (patent pending).
- Recognize that the problem is humanity as a whole rather than just segments of it.
- Realize that nothing will ever change it because it's a matter of human nature being awful rather than just society being awful.
- Resign yourself to having to put up with all the bullshit until your dying breath.
It's a rather pessimistic point of view, but hey, at least I'm not constantly stressing over how shitty people are. Also, for the record, this is probably not something you should actually strive for. It's a half-joking suggestion I'm making just to share my own way of dealing with the knowledge of all the ways in which people suck.
I dunno if any of that will actually help you out, but I tried. Maybe someone more optimistic will come along and give a you a better take on it all, haha.