Well, despite the above posts, it can be a problem. We had a Danforth binnacle compass on our previous boat, purchased in SF and nominally being compensated for that latitude.
As we approached New Zealand
in 1990, we noticed the card tilting more and more. By the time we reached about 32 south it began to hang up, and by the time we were in Auckland
it had ceased working due to excessive dip. Interestingly, a fellow SFbay sailor who we had been in company with and who had a Ritchie compass had no problems. We were able to have the compass re-balanced in Auckland
, and chose what they called an "equatorial" balance, and it seemed to suffice for the rest of our voyaging in that boat, but we never got very far north!
So, it seems to depend on the specific model that you have on your boat because they vary in their susceptibility to dip angle changes.