We often argue about issues that she thinks are not worth fighting about. I feel that I need to get my point across, but she won't listen if she does not feel that the matters are worthy of a discussion. Any ideas?
When you have differing viewpoints with someone close to you on an issue that concerns you, it's very important to at least feel that you've been heard, and that your points have been considered. Generally speaking, when people are faced with the decision between accepting a new idea or fighting to hold on to their old beliefs, most people choose the latter. I think that can be a defense mechanism for a lot of people without them even realizing it.
Your mom may feel very strongly that she is right on these issues, and that any debate about them is just silly. The best way to get her to listen to all that you have to say without interrupting you is to write it all down in a letter and give it to her. You could start it by writing something like "Mom, something has been on my mind and I'd really like to try discussing it with you again. I wanted to approach it with you in a letter because I didn't want it to come across as a confrontation.
You could go on to explain that it's important for you to feel like you've at least been heard. If you wonder why she is so quick to dismiss the issue, or feels so strongly about it, ask her. Hopefully, this will help her to see your viewpoint more objectively, and avoid a confrontation.