For me, it is very important, but only when it comes to my absolute closest friends, of which I have only six: my best friend, her husband, my brother, Destiny, my mother, and my significant other. Fortunately for me, they all resoundingly endorse my significant other, though sometimes he himself is somewhat bashful in this regard.
There was a time, or times, or several, or nearly all, occasions, really, when I had stubbornly, defiantly, and blindly stood by my most recent paramour to the concern and trepidation of my support group. It was this experience, however, that taught me two things: 1) how to identify real friends--they are the ones that stick by you even through the worst disasters but without condoning your bullshit. 2) how to identify a good candidate for a significant other--they are real friends.
I am not sure how precisely relevant this information is to your situation since your issue is with your s/o's friend. But it seems that it is also an issue with your s/o if he is not accepting of the boundary you have drawn in this instance.