Plumbing – Do I need teflon tape (or something else) for a plastic shower head

My favorite pipe thread sealer is RectorSeal #5. Here's a link. I see according to its datasheet that its rated for steam pipes. You might have to let it dry a little while before pressuring, but after that its good for 2600 psi.

As long as the shower head inside diameter is a standard size (which I imagine it is), you really should be able to find a washer with a built-in screen at your local hardware store (although I haven't tried myself so I could be wrong).

And still if you can't find one then you can just go with a standard washer without the screen. (And maybe you could remove the screen from the broken washer and place it underneath the new standard washer that you just inserted.)

I think the screen in a shower head is not so much for aeration as to prevent contaminants from getting into the shower and interfering with the various spray patterns.