Six years?
Is there a reason behind the avoidance? Like, some kind of addiction or something like that?
If there isn't, you gotta make a choice. Even if there is you gotta make one, but it would be understandable that your family was resistant.
Me? Barring something major, if you love your girlfriend, you either take a stand now, or you're essentially telling her you don't really care. I'm sure you do care, just maybe not enough to make it last.
Besides, if you're an adult, there comes a point where you have to set your boundaries. You have to make the choice about whether or not your family has a say in your choice of partners. Moreover, the sooner you set whatever boundary it is, the better. Fuck Christmas, because if you don't do it soon, it'll be every holiday that you and whoever you're with is being judged, with your family's opinion of your partners mattering more than your own. This will severely fuck with any partner you have, even the ones they do like. That's just how it works until the child stands up and says no.
It'll always be your family deciding who is and isn't good enough, and that isn't something that is hard to pick up on when you're coming into it from the outside.
There may well be reasons to not make this GF your hill to fight for, I dunno. But after 5 years, if she isn't, then wtf are you doing with her still?