Is this configurable? To disable all mobs/entities besides players on a server? I've heard about CraftTweaker but I'm not sure if it can be changed there

No, it is not.
Please do not necropost, and instead use our Discord to receive support for the mod.

Can you please go into as much detail as possible? What doesn't work? What do you do? When do they work/not work? I'm assuming you're using 1.12.2 and v1.8.4.1(if that's not the case, please tell me so).

So when an animal steps on a mine it doesn't blow up in my private world and I only use the latest version of both Minecraft version and security craft version

Works for me. https://i.imgur.com/Or9Xmvs.mp4
Sheep, cows, pig, villagers etc. work as well.