So I'm finally able to watch anything involving Marvel Thor and just tell myself "It's just a movie. No reason to get hung up on the details"
But I still come by some people who only know the myths through the movies and make comments that just make me go nnnnggggg.
"I think some Norwegian myths or something said Loki was Odin's son"
No, I will repeat this forever, Loki was Odin's blood-brother (they cut themselves and mixed blood, making them official "real" brothers by Viking tradition). Loki was Thor's "uncle". Again, you can enjoy the movies/comics as much as you like, but it's silly to try and change the myths to fit them.
"According to some myths Frigga taught Loki his magic"
Again no. Jotuns (ice giants) were by default able to preform magic, and the myths very clearly say that Loki learned it from other jotuns.
If you want a plot bunny for your next Thor fanfiction however, this should do. The Vikings considered women to be magic, men not so much. It was seen as unmanly to even try, and it would seem like it was fairly common to believe men couldn't even do it properly. The only other god who does magic is Odin who was taught in secret by Freya, and he mixed blood with Loki...
So the fact that Loki could so easily do magic could have caused some serious suspicion by everybody who wasn't in on the adoption secret in the movies, not to mention Loki feeling like a weird effeminate "freak". Basically, to Vikings a boy who showed signs at being good at magic would be like a boy menstruating (showing signs that he could get pregnant, which Loki of course also did plenty of times)
So yeah, I suppose my point is that if you feel like taking from the myths by making Tom Hiddleston Loki a gender fluid pansexual, go nuts. Just please don't do it the other way around by getting into fights with people over if Loki was Odin's adopted son in the myths or not. That will just give poor Scandinavians headaches and that is, like, super cruel.