Well, in the U.S., as you know, that "independent" thing just means that you haven't registered as a member of a political party (in my country, most people don't join with the party, it's only been in recent years that we even have anything like a "primary" where party members can vote for party leaders... it used to be done by delegates at conventions). It says nothing about how, or if you vote and it says nothing about your socio-political stance if you aren't a member of either party.
From what I got from facts, and reading between the lines is that the shooter was more of an alt-right poster in right wing groups. He comes from a Mormon, Republican family where "leaning left" can mean simply criticizing their ideology and leaders. The etchings on the bullet casings were in the style of
Groyper memes, with video game references. Also gleaned... Fuentes came out pretty quick and disavowed this guy, and those that engage in political violence, where he's all but encouraged it before (they were active at the Capitol on Jan 6). He knew this guy had Groyper associations.
I also believe the shooter may have had some cognitive dissonance, having a close friend (texts kind of indicate possible intimacy?) that is trans. That's my viewpoint only, based not on facts but human nature.
None of this supports the narrative that these bullies are trying to push, to start a war to eliminate the Democrats (that are only really on the "left" in context of U.S. politics... they'd be too conservative for my voting pen, in Canada).
These appointed, anointed assholes are just drunk on their own power. For example the head of the FCC that Trump put in place is now threatening Disney, because a network they own hosts political comedian Jimmy Kimmel, who went against their narrative that the shooter was from the left. "We can do this the easy way or the hard way. These companies can find ways to take action on Kimmel or there is going to be additional work for the FCC ahead."
P.S. Just heard that Jimmy Kimmel's show has been indefinitely canceled. Almost every corp. is a lickspittle for Donald Trump now. Nobody else gets a broadcast platform but those that promote their doctrine.
This is all Kimmel actually said about Kirk:
"We hit some new lows over the weekend with the MAGA gang desperately trying to characterize this kid who murdered Charlie Kirk as anything other than one of them and doing everything they can to score political points from it," Kimmel said.
That's not even a joke, it's the truth. This is a text book example of "speaking truth to power". Something that the 1st Amendment is supposed to protect.