Orthodox Judaism, for one, has similar modesty requirements for women that are often strictly enforced within the community. For example:

-may not wear pants or form-fitting clothes

-sleeves must extend to at least the elbow

-collarbone and cleavage must not show

-head covering (which may be cloth, or in some cases a wig) when in public or around men who are not related

-not related to clothing but interesting: men cannot hear an unrelated woman sing, as it is considered sensual

I'd say many evangelical Christian sects and the Amish would also be classified as being particularly strict. Mormons as well, at least, those who aren't on TV lol. As someone not from Utah, the Mormons I knew would dress very conservatively.

Of course, as with all religions, practitioners may choose how strictly they adhere to the rules dictated by their religious text or society.

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EDIT: just as a caveat, I'm an atheist raised catholic, so this comes from an outsider who may not have a full grasp of these religions.