Ok guys

Not playing records, dust  cover on.

Playing records, dust cover off.  

I can hear feedback at significant volumes with cover on, so easy choice.

Wolf how is a dust cover going to be a bass trap? Do you know what the wavelength of 20 Hz is?? The wavelength of your dust cover is 800 Hz or so. But none of this determines how your dust cover resonates. If you have a flimsy dust cover directly attached to the same platform your tonearm and bearing are mounted to and that platform is not sufficiently heavy, stiff and non resonant. You might indeed have a problem. Correctly made dust covers and turntables like the SOTA and dust covers that are not directly attached to the turntable improve the sound by attenuating the noise (music) in the room by about 20 dB depending on the cover, like having hearing protectors on. 
Now If you have static in your dust cover lifting your tonearm you need to throw the whole mess away and start over. Better yet switch to digital only. But then I guess you'll get paranoid about something else.
If you really think your dust cover causes sonic deterioration you also need to throw the whole mess away and get a decent turntable. Protecting your records is the first priority, sonics second. But Like I have said repeatedly all the turntables I have had in the last 40 years have sounded better with their dust covers down. I guess I know how to pick them or is it just dumb luck. 
I love you guys who complain about static and spend thousands of dollars on record cleaning junk. I use conductive sweep arms and dust covers, get better sound and I never clean a record I have owned from new. Never have to. The secret to cleaning records is don't let them get dirty. 

dust covers that are not directly attached to the turntable improve the sound by attenuating the noise (music) in the room by about 20 dB depending on the cover, like having hearing protectors on.

Wow 20dB 🤯.....here's the miracle sound-proofing material the world has been waiting for.......1/8 inch acrylic 🥳
And no proof required...🤣
Wait till I notify that village looking for it's inhabitant.....that he's been found 🤥

It’s a cavity resonator, it’s a Helmholtz resonator, it’s two, two! mints in one!!  🤗

Halcro, I have a decibel meter. My SOTA does 18 db down, the SME 25 dB. It has a thicker cover. The difference does decrease a bit with louder volumes. These figures are at 95 dB. Most good  hearing protectors come in at 25 to 30 dB and what are they? A thin plastic shell stuffed with a little foam with a seal fitted. Geoffkait, a Helmholtz resonator requires a throat (opening) Do hearing protectors resonate? Sorry, no mints at all.
I keep meaning to run a test record with a frequency sweep to compare attenuation at different frequencies. I will report when I get it done. Of course I can not be sure what other dust covers will do. Depends on the design. 
 halcro, most house walls are pretty resonant just bang on one. Now go into the next room. What happens to the sound? And the door is probably open. Now close the door. What happens. The dust cover is another room with a closed door. Some miracle ha. 
You guys crack me up. Assumptions are the mother of all ---- ups. If I say the word my post will get deleted. Assumptions based on mythology are fairy tales.