Cannon filter on Nikon?

If the OP was asking about a UV or skylight filter, your answer  might be a pertinent. Those filters are often used to protect the lens. But she was asking about a polarizer that is designed to effect certain attributes of the image; such as making a blue sky darker blue, or reducing reflection when taking a picture thru glass.  Using filters specially to effect the image, has been done since the days that the only color of images was black...and white. There is nothing wrong with using special effects filters, such  as polarizers, and neutral density filters.

By the way, a lens doesn't always have a hood protecting it. A for instance is when the lens is in the bag. Twice, I've had accidents with just the lens, where if I didn't have a protective filter on, the front element would have broken. I agree that a lenses' performance is effected by a placing a filter on it. The question is, do you want that effect? If not, then take the filter off.