I think as a list manager you have every right to say I don't want this or that kind of post and take action if you see them.
I strongly disagree with your take on this though, referring to you as not a list manager but as a regular member. My personal opinion is that this certainly has nothing to do with spam or chain letters, and doesn't conflict with praying for those nearer and dearer. I don't see how it could be anything but helpful (minus a few kooks who could hijack anything for selfish purposes.) I do see how someone could see it doesn't really apply to music, or that objects of the requests are not closely enough related or something like that, but in general, I think they are very valuable. you have people around the world praying for a little baby. What is the harm?