No. Villagers can not open gates but can open doors.

Can Minecraft pillagers open gates?

Pillagers are still able to open doors just like villagers, and unless you're planning on waiting them out, they don't just give up willy nilly. If you control where pillagers will be, it's a lot easier to deal with them when and how you want to.

Can mobs open gates?

Fence gates are ideal for added protection because zombies cannot open them. Other hostile mobs, such as skeletons and creepers, cannot open fence gates either.