There are a few tools and scripts that will let you paint symmetrically in the world-space. Mari can also paint mirrored to some extent. It is only supported in the buffer, though. This means that you might find it tough to paint on opposite sides of a model in the viewport. There is a way to flip paint, though.
VFX veteran, Mari expert and Lighting TD Peter Aversten dives into a discussion / demonstration of UV strategies in Mari. The first part has a look into how you can mirror paint in Mari without using any fancy 3rd party scripts. You can essentially flip paint by implementing some UV strategies ahead of time.
Aversten shows how you can utilize the UV layout of your objects to flip paint. This can work on any object that is symmetrical in Mari 3. There is a lot a look into using the patch linking procedure as a method to sync up paint from one side of a model to another. Looking forward to the other parts of this topic!