In an investing context this might be different. Personally I do check the public data regarding top executives of companies I consider for investment. For instance, Elon Musk has had a continuing record of success in difficult and improbable cases from Zip2 on to even The Boring Company. Hence I tend to be cautious before damning Twitter.
Otherwise consider the bench strength in Engineering, design and finance. For every investment I always check Finance because liquidity issues determine ultimate failure ro survival, just ahead of Free Cash Flow.
So, if a fool or two decides that a CEO's purported political views is more important than business acumen, so be it. Rationally trying to typecast a given CEO, in particular Elon Musk, is fraught with inherent danger. After all, he's also beset with antagonistic bots, is he not?
OTOH, he does seem to rather enjoy provocation...he knows that generates many clicks.