I've found that card covers come in slightly different sizes,some will take a paper sleeve others won't. I usually snip the corners of the paper sleeves at 45 degrees which makes it easier to insert into the card cover. There was a thread on here where someone recommended inner sleeves that are rounded. I bought some of these but have found the same problem, it all depends on the outer cardboard sleeve. It would appear that the few mill difference on the outer is the deciding factor. I've bought sleeves from several suppliers over the years sadly never taking notice which is the best fit.
I just looked ,if you put "stiff white card sleeves" in the search box you'll find some recommendations there.