Given the "hate" quote, I wouldn't be surprised if he had left leaning beliefs. But does it matter? Conservatives were practically running with the trans-shooter narrative before his body even hit the floor. And for those who aren't complete fucking morons, most understand that the only people who commit murders like this are mentally unwell which vastly overshadows whatever their voting preferences are.
There's something to be said for conservative rhetoric appealing to and amplifying such delusional people, which may be why the vast majority of such violence is perpetrated by rightwingers. After all, a sociopathic lack of empathy contributes to both violence and bigoted worldviews. But they're hardly causal, essential, or exclusive.
A crazy terminally-online white kid with a gun shot a racist fascist asshole dead. The reaction from both the right and the left is influenced very little by any other facts. Some people are sowing chaos and it's working. Most don't have the time, ability, capacity, or desire to sort through the mess and evaluate nuances and uncertainties: they're just running with whatever fits their biases best. Not only does the truth not seem to matter, but what conclusions they're drawing also doesn't seem to matter because they already had them. It just nudged everything forward by a notch.