The Strat pickup is probably fully wax potted, and it's the wax that's holding the cover on. It could be glued on, but that's very unlikely.

It should come off with constant prying between the base plate and the cover. If not, you could try heating it up with a hairdryer until you start to see melted wax dripping out, and then you can quickly pry the cover off. But it needs to be pretty warm to do that so it may distort the pickup cover and some thin latex/PVC/nitrile gloves are recommended to give at lest some protection from the heat whilst allowing you to grip firmly.

You won't damage the pickup provided you use just enough heat to soften and just start to melt the wax. You can of course try pulling before you see any melted wax, as it will soften.

It could be that it's just the windings and the tape that are pressing against the side of the cover. With a stacked pickup, you've got to fit two coils in the space you normally fit one, so the windings will occupy all of the bobbin capacity. If it is a proper SD stacked pickup, then I can't see them ever gluing the cover on as it would make the pickup unrepairable. So I'd strongly suggest either wax, the cover being pushed on over a very fully wound bobbin, or a combination of both.