In regards to women, the books have been much better about that in recent years. Not to say the mandalorian is doing "worse" though. I'm sure we'll see a fair amount of representation once other characters are introduced.
a friend of mine is real down on the portrayal of their culture, having preferred what was shown in the karen traviss novels, which had many details soon retconned by the clone wars cartoon.
Gonna nerd out cuz I have time to kill. None of this is all too related to the show though. So here's some light backstory as it goes in the current canon. The mandalorians had a planet to themselves, Mandalore, shown off in the clone wars cartoon but introduced very long before. After the fall of the republic, there was great pressure from the empire for the mandalorians to cooperate or suffer the natural imperial consequences. By about the time of A New Hope, several houses (they have clans and such) joined up with the empire, most pragmatically, but some refused and scattered or were absorbed/wiped out. It has not been told of yet, but somewhere between the rebels cartoon and The Mandalorian, their society and homeworld appears to have suffered greatly. Through dialogue in Mandalorian's episode 3, it was likely a result of the empire very harshly stamping out resistance. As of now, with this story taking place 5 years after Return of The Jedi, the situation is back in line with how mandalorians were portrayed in nearly every other canon source besides the old books/comics in that kind of ghetto between 2004 and 2012. (I'm not very fond of the mandalorian portrayals in that time)
Now on a tangent, used to be boba fett was the only definite mandalorian running around. As of the new canon, certain fans seem to consider him kind of pretender because, in the clone wars cartoon, Jango is denounced as non-mandalorian, some criminal who found the armor, so boba doesn't have the claim either. But he is named this by a corrupt government official who said and did anything to win support and keep ahead of others.
People often cite this as definitive proof that jango is not mandalorian (Semi-true, as he comes from their colony, Concord Dawn, which is also where the NZ accent is supposed to come from) and since boba is a clone, neither is he. This is the thing about star wars fans, where analysis of every line of dialogue and exposition, every background prop or character, is taken too far and too literally. (I mean yeah I go crazy, but I see room for interpretation where things are unclear) I think his status within the society was shaky, but I believe jango was mandalorian by association at the least, which is how their martial culture has always seemed to work and as it seems to work now (with talk of foundlings in the show, likely being their term for adopted children).
If this spout of nonsense tells you anything, it's that star wars canon is a mess and it's quite fun for us to see unfold.