Today, the Swedish word for their belief is asatro, where as is male deity from the era in question and tro is belief. (Female deity of same era is asynja)
Is it really refering specifically to a male deity? I thought it refers in short in general to the Æsir, one of the principal pantheons, with male and female gods
Asatro in many places has a strong negative connotation due to partially being coopted by racists. I've encountered more purported believers in Asatro who are neo-Nazi than not. They may well be a small minority for what I know, but they are vocal, and so it's a term that's tricky.
That is a form of historical appropriation that we should not just blindly accept. The word originates in the 1820s and the word as is much older. I for one will use it in its original meaning and encourage others to do as well.
I get that sentiment, though I feel it's a bit of a losing battle, because it also means you may often need to contextualize what you mean if you want to avoid misunderstandings
https://en.m.wikipedia.org/wiki/%C3%86sir