Personally, if I were on Team Caveman, I'd want to BEFRIEND the Kingdom of Science instead of fighting them over ideological differences.
With Tsukasa's physically able army of hunters and Senku's lost scientific knowledge the new human race would thrive, and if the two were more willing to find a middle ground in their beliefs they could potentially create a far better world than the old one without giving up things like life saving medicine and scientific curiosity.
Of course most human conflicts (both ideological and physical) in life wouldn't exist if people thought about things logically and empathetically, and this show is hardly any different in that regard. Everyone does what they subjectively believe to be "the right thing to do", and they follow that belief absolutely, even if it means needlessly butting heads with other humans.
Also, if I were on Team Caveman, the wave of instant kill gas would scare the fuck out of me.