I'm scared to ask, but if it's really not that weird, then why do people sometimes get angry or creeped-out when I ask them to contribute to my project?

I mostly second what others have said. Its your coping mechanism. Bringing other people into it isn't fair to them. Like others have said, people have their own emotional issues with lingerie. This is different than a teddy bear, because people don't buy and/or use teddy bears for sexual reasons. People find it off putting because of the sexual nature of women's underclothing, and that you are doing it to cope with sexual abuse, and also apparently telling others about it, and involving them. Many, many women have also been sexually abused, and these may be the very women that you are asking if you can cuddle with their bras at night. I second what others say, find your own source for these, and stop asking people for theirs. You may find less kickback, which will stop the embarrassment over it.

Feel free to keep doing what helps you get through the night. There may come a day when you don't need it any longer. Keep going to therapy. There will come a day when you can talk about his event like it never happened. I highly recommend EMDR therapy. IT helped me with my own trauma, and I have friend who have had great success with it as well.

I wish you good mental health.