This is well-intentioned but wrong. The vast majority of academics in my field have no social media presence, express zero political views at work, and spend their day trying to understand and cure disease and train others to do so.
Their apolitical truth-seeking is not, however, seen as a counter-balance to politicization of academia. It is simply not seen *at all*. The public has no idea who they are, and forms their opinion about academia based on random social media scandals, congressional hearings, or interviews that go viral (usually because the academic being interviews was particularly clueless).
The upshot is that it does not take much to change individual perceptions. U Chicago and MIT have shown that people will form strong opinions about which schools are truth seeking based on a handful of symbolic gestures by the president, described in the right language. Better media training and thinking more strategically about visible academic positions would go a long way.
Academics should be aware that their efforts to change public opinion not only failed but backfired, and should now attempt to change public opinion back to believing that they're hunting for truth rather than changing public opinion. Best way to do that is by hunting for truth.