Only the very top of the treble range is effected. Toe them in a little more toward you to compensate. or cut a little hole where the tweeter goes.
Guilford of Maine makes acoustically transparent fabric for covering furniture, acoustic panels, etc. Not meant for speaker grill though.
https://acousticalsolutions.com/wp-content/uploads/2015/01/D-Guilford-of-Maine-FR701-Acoustic-Fabric.pdfIt is pretty transparent to sound, but I did use color samples of it to hang in front of overly bright tweeters to knock them down a hair.
Slightly better WAF than tissue paper.
I saw the ad for the Parts express stuff. That's probably even more acoustically transparent because it is thinner and seems less opaque to light. It's seems like more plasticky, less cottony than FR701, so maybe less absorbent?
Will you build a frame from wood, or try that frame kit from PE?