I'm on Propranolol currently and no mental side effects. Propranolol is not originally meant to treat anxiety. It's for heart and blood pressure issues. Doctors noticed it can be used for anxiety as it calms your body down. It's been an absolute lifesaver for me!
Keep in mind it will only tame your physical symptoms. It will actually do nothing mentally, your anxious thoughts will still be there. But this certainly won't make them worse.
For me over time it's making them better, because I was left with only being anxious about being anxious. And the fact my body has felt quite calm for 2 months now, is making my anxious thoughts less.