The issue I see with using Bayesian theorem in current day politics is one thing Dev has (poorly) addressed and one thing he has not
1) The effect of lack of information. Dev has simply replied with "well, when we find out that new information, that can change your mind." Problem is, that is dependent on the information coming out to the public within the time frame of interest for the event/the willingness of someone to actually engage and deal with that information. Problem is, in current day, that isn't happening that much, and no amount of "well, give more info/make it more accessible" is really helping.
2) Malice. The general issue here is just how much current day ideologues lie/tell-half truths out of a malice against the other side. Problem there is that includes giving fake info that doesn't help with "Bayesian analysis" for normies, but instead hurts it. If the only answer to that is "wait till the real information comes out", we're fucked 8 ways to Sunday because of how long it takes for actual info to come out on the event, if it even does.
Honestly, I feel Dev's video has a good point, i.e. weighing evidence and keeping one's mind open to changing if some probable evidence comes in. On top of which, the guy explains Bayesian theorem easier than what I had back in college.
The issue is the theorem does not map as well in subjective real world socio-politics due to a lot of factors Dev has not addressed/addresses poorly. The theorem is difficult to work in outside of a qualitative level.