Water supply line to toilet. The water supply water stop is mfg. by Brass Craft. Instead if a handle to turn in order to shut off the water there is a plastic cap. It can be removed to expose a plastic square about 1/4". I am afraid to break it, as I'm not sure I could stop the water flow. How do I activate this water stop?

If this is a clear plastic round handle with ridges around the edge, then that is the handle for the stop. If your water is not real corrosive then it is possible that you might be able to turn the valve using this handle, if not then you can remove this handle and use a small wrench on the 1/4 inch stem, try to turn it very gently, if it does not turn I would suggest you replace the complete turn off if you have the know how.

Water supply line to toilet. The water supply water stop is mfg. by Brass Craft. Insted if a handle to turn in order to shut off the water there is a plastic cap. It can be removed to expose a plastic square about 1/4". I am afraid to break it, as i'm not sure i could stop the water flow. How do I activate this water stop?

Would this be BrassCrafts new 1/4 turn stop with a plastic handle,(see image)
Instead of a metal one? What do you wish to do turn it on or turn it off?
This valve only turns a quarter turn so please explain what your problem is. Regards, Tom

Those are flimsy angle stops and frequently leak. We don't use them at all. As other suggested it - replace it with metal angle stop.