Hmm… I’ve used webcam covers on all my MacBooks (Air, Pro, MacBook), and haven’t noticed a problem with this.
It might depend on the model? I’m tying this on a MacBook Pro, with the webcam cover in place. If I put my thumb slightly to the right of the webcam, that triggers the screen brightness change. But the cover alone is fine.
Or — perhaps more likely — it might be that you need a smaller webcam cover? I use these (currently showing as unavailable), as they are both very small and very thin (so don’t affect the unit closing properly): https://www.amazon.co.uk/gp/product/B01J8UO94U/