Yes—an alternative cap style may help. From the answers, the most likely issue is that the spring-loaded center-pinch cap can be pushed inward enough to contact the filter glass, especially with a slim filter or if the cap isn’t fully seated.

Safer options mentioned were:

• push-on caps
• slip-on / over-the-lens caps
• for unusual setups, a step-up ring with a larger cap

A slip-on or over-the-front style cap is the simplest option because it avoids inner tabs pressing near the glass.

Using the broken filter as a permanent cap mount is not recommended. Repeatedly screwing a damaged filter on and off would be awkward, and it could increase wear on the filter or lens threads over time. A chipped, non-rotating polarizer also isn’t a great part to keep handling.

So the practical answer is: replace the damaged filter, and use a push-on or slip-on cap if you want to reduce the chance of the cap contacting the filter.