Actually, when I was starting with React, then for a while Talkyard did use both jQuery and React on the same pages (not a good idea, I agree). I was careful to avoid the bugs you have in mind from happening, so that wasn't a problem,
however, loading & using both libs wasn't good for performance — just parsing and executing the 30 kb min.js.gz jQuery bundle took maybe half a second? a second? on mobile phones, back at the time (2.5 years ago).