I just installed a polarizing lens filter on my 150-600mm telephoto lens last week. This week, I was photographing birds by boat when my camera strap slipped off my shoulder and fell to the deck, lens first. I tried the camera out, and it seemed to be shooting fine, despite the cracks.
I just got home and took off the filter and the lens is fine! My relief is palpable. If you have been putting off adding a filter to your expensive lenses, I really recommend it.
That was the first thing, skylight or pol filter, that I bought the time I used full cameras with different lenses.