You can mix film and developer brands as much as you want.
If you consider that there are lots of manufacturers that make chemistry, without making film; well, they wouldn't be doing that unless there was a market for it.

Your choice of film and developer should be made based on the lighting you work in, depth of field and aperture you want to shoot at, and most importantly based on your output. It has to be geared to suit your process, whatever it happens to be.