It's very difficult to change the ways of people, especially as they get older. I read somewhere that when a person reaches the age of 36, the will accept 96% of what they have learnt as a given and will never change their mind to opposing views. From experience this seems pretty right.
It is also common for people to put others down to make themselves feel better, often because they themselves have low self esteem issues and therefore such remarks generally have little to do with the people who are actually being attacked. I decided long ago to try as much as possible not to care what people think or say about myself or others. I've found when I do I just get really upset and people rarely listen anyway.
For a long time my dad had a similar thing with racism, it bugged me but I knew that he had been conditioned over decades to think that way. Over time he toned down as I dropped little hints whenever he made a racist remark. If like me, you have trouble with emotions, this makes the situation even more difficult. From what you have described I would expect that your mum has been like this for a long time and will not change overnight.