Do you know any stores in Metro Manila which sell ethnic handwoven products for moms and babies--like, diaper bags or baby carriers?

I know online stores that make baby carriers out of ethnic fabrics. Try Quality Brand, Nanay at Ako and Lelliebubb. As far as I know, the do wrap conversions. As for diaper bags, you can try Fluffy Pwets. Not really sure if they can do diaper bags but they have this Ship Your Own Fabric (SYOF) option and they can turn your fabrics into tote bags, diapers, clothes, bibs etc.

Kultura has a wide range of ethnic products that you can checkout. They have a wide range of handwoven/handmade items such as different bags (you can choose from bags made from different local materials), baskets and pouches that are also very fashionable. For baby carriers, they are mostly available online. You can try checking out Saya, Next9, Beco Gemini, etc.