Why do my towels smell bad after washing?

I’ve been struggling with an annoying issue: my towels smell musty even after washing them. 🫤 They’re clean, but the smell persists, especially when they get damp again after use.

Here’s what I’ve tried so far:

• Washing them at high temperatures. (it seems to work, but then is it the towels quality?)

• Using fabric softener (someone said it might be bad, though?), using vinegar.

• I don't have a drier (or access to direct sunlight).

• Cleaning the washing machine regularly.

Nothing seems to work! Could it be something in the washing process, my detergent, or (I suspect) the towel quality. Any tips or tricks you’ve used that actually work? Also, in case the towels are the issue, what type of material would you recommend for future purchases?