Personally I think if we're at a point where cases can be thrown out because people on social media post about them, we need to rethink how we deal with prejudice in the courts in the social media age. It's one thing to control a semi-regulated press - quite another to control everyone on the internet.
Anyway, I think driving 300 miles with a pole/bar to kill someone indicates that it was a targeted killing. I don't know why they'd pre-emptively say no evidence of a political motive if they just mean they have no evidence of ANY motive and are keeping an open mind...
There have been several killings recently where there's been some effort to claim that they weren't "political" because the killer had an uncertain or mixed ideology - but they were clearly radicalised in some way. Like the guy who killed Charlie Kirk - he was clearly extremely online and active on discord and targeted him personally because of Charlie's opinions/activism, but because he wasn't clearly a Democrat activist either people said there was no political motivation. It could be the same here, maybe this guy won't come out to be someone who targeted her because she was, say, a Reform political party spokeswoman, but Bluesky told him she was a danger to trans rights or something. Which is political but not party political. (I have no information on this, just speculating.)