If it had been Dave Rubin or some twitch streamer or that antisemitic Times Square Elmo they'd have probably reacted the same. The right-wing response to his death seems like it's more opportunistic than genuine, while the liberal response is the kind of shit they say about any generic republican who dies. It's hard to judge the staying power in the moment, especially if the media downplays the seemingly fascist shooter and limits the news cycles this makes.
He was a white house insider but I don't know what degree of influence he actually had there because he himself was just a generic meat puppet for his billionaire funders. As a media figure I more or less forgot he existed until last week when I saw a DSA post about his tour. As far as I know there wasn't even going to be a counter-protest, just an alternative event which would have drawn a larger crowd. The cultural relevancy of those is stuck in the 2010s and now we have terms like "debate pervert" to stereotype his brand of Guy. Even the memes about him were stuck in 2018 and limited to small face+diaper. I'd consider him more relevant than Dave Rubin or Stephen Crowder, but a C-tier influencer compared to Ben Shapiro/Tucker Carlson/Alex Jones/Joe Rogan/streamers. What little I saw of his media presence anymore felt like decade-old boomer slop.
Even between those A-tier influencers, none of them seem individually important enough for a leftist to target. Shapiro is on the decline, Tucker is deplatformed, Alex Jones is a donkey of the week for one of my favourite podcasts, and their streamers keep getting outed as paedophiles. Any other culture warrior name I can think of is just some dipshit who will be replaced tomorrow by another dipshit saying the same things they've been saying since the 1930s.