I'm trying to take the cover off of my fluorescent fixture, but I can't seem to figure out this fastener. I've tried rotating it to no effect.
Turn it 90 degrees and it will release same with the one at the other end if it has one.
Turn it 90 degrees.
As you turn it, you'll find one position is more relaxed (sloppy) than the other. That is the release position. It goes into an oval hole in the upper part.
It may take some rattling to get it to let loose, or possibly prying. Sometimes the leaky tar from the ballast glues the lid on.
Those lampholders are done for. The one is broken, but most likely the plastic is fatigued on all of them and they are all fragile. That's a standard lampholder type and they cost as little as 60 cents apiece at 1000bulbs.com. That's a normal/tall type intended for T12 bulbs, if you're switching to T8 you can stay with those or use the shorter ones. If you're going LED or rapid/programmed start ballast, remember to get non-shunted type.
Honestly I think the best light available today is actual fluorescent tubes, driven by an electronic ballast, either the T8 90+ CRI (at your choice of color temp). Or the T12 98 CRI type.
Rotating it into alignment (quarter turn) is the normal procedure.
If it still won't come off, then just use a screwdriver in the center to pry with.
They are made to be able to snap into place even when not aligned and the screwdriver can bring the two sides together enough to pop it out. It is made of spring steel so you are unlikely to break it.