Your mother's racism might ease or change over time as she begins to see through your experience that it is misguided - but it is shocking that it is to a degree that she would openly make comments in front of your girlfriend, so it's possible that it never will. Having a hateful/racist mother in law can put a great strain on a marriage. This was my mother's experience; it caused her such anguish over the years (including mother in law sometimes turning father against her) that she warned us daughters not to get involved any further if we realise the Mother in Law doesn't like us. I would have ignored that for the right man, luckily I didn't have to.
This might be something that you will just have to manage for the rest of her life. You could cut her out, which would make things difficult for you and the rest of your family, or you could end up dealing with having to call her out on it time and time again. Of course you must never sit back and accept it, but I tend to take the path of least conflict by trying to avoid unresolvable issues altogether as much as possible and only speaking up as much as is necessary.
Explaining, debating, trying to make her think about how her views could be wrong, beauty ideals being subjective, the qualities of your girlfriend as a person meaning cultural differences are only an enhancement rather than a hindrance to how your relationship actually works and refusing to accept any insulting comment as okay over years and years, while also reminding her that this doesn't fit with how she generally views all other situations might start to make her see that there is something wrong with the way she sees things.
But it might not.
Since you can't change who your mother is, or who the love of your life is, it will be something you will just have to manage in whatever way seems best to the both of you. If it gets to a point where is is seriously damaging your relationship, you may have to cut her. The families we build are the future, they come first. But the families we are born into are important source of sense of self, security, support and education so... Difficult situation.