I am certain these are 30's and 40's fabrics. I have some old tops that I know are from that period, and there are some of the same fabrics.
You can certainly save this top by quilting it. Where the seams are frayed and coming apart, you can do a narrow zigzag stitch of the seam in a matching thread. Even if it's visible, it is really necessary to hold the top together. It's my easiest and most effective "fix" for this particular problem.
This is certainly worth saving. It is a really nice top. Yes, I am certain this is from the late 30's to early 40's. Not 50's...fabric changed after World War II..much more modern patterns.
You have a nice top there...do what you can to save it. It'll be worth it.