I've never had a problem with this. London in the 80s was awash with cyclists who wore anti-pollution masks. They just ended up looking a little silly. The sort of thing you used to wear when treating timber for woodworm. Daft on a bicycle.
I wear glasses to stop insects, rain and grit from hitting my eyes, which can be a problem. I get maybe two or three flies in my throat per summer and it's not a problem. One glug of water and it's forgotten.
I've always hung my jaw down when climbing hard, in the odd belief that it makes a bigger 'airscoop'. I tell my kids to do it too. I have no idea whether it works or not, but it doesn't seem to make me into a fly trap.