using comma within the appositive

Solution 1:

Yes, it's correct.

However, some people could think it was confusing. Stylistically, you can always use different punctuation to indicate the appositive if the commas concern you:

The factory processes different types of ropes (such as cotton, acrylic, nylon, etc.) from garment waste.

The factory processes different types of ropes—such as cotton, acrylic, nylon, and so on—from garment waste.

But there's nothing grammatically wrong with the sentence as you had it.

(Note that in my second revision, I replaced etc. with and so on. This is because some style guides, such as The Chicago Manual of Style, recommend only using etc. inside parentheses.)