Is there a way to make it where I can disable or at least fight enemy culture/influence? I was beating the sophons on hard mode last night military wise, but their culture was better than my vodyani culture.  I am not seeing a tech to combat, negate, or mitigate in any way.

Culture spread is done by influence, and it won't actually take over your planets unless they've researched a tech to do it (which is in era 3, so if it's before that don't worry).

Fighting back is mostly just pumping your influence output (purple star).