Textiles generally do not fall within the scope of CE directives and do not require the CE mark. What is actually needed: REACH (SVHC notification + restrictions under Annex XVII such as azo dyes, formaldehyde, nickel release, etc.), fiber composition labeling regulation (EU) 1007/2011, GPSR General Product Safety Regulation, as well as customer-required RSL reports and OEKO-TEX certification. If electronic components are included (such as heated clothing), the complete product needs CE's LVD/EMC.
This is a typical misconception of "CE universalism": many product categories are simply not within the scope of CE, and forcing CE certification both wastes money and fails to solve the problem. The basis for judgment is always whether the product falls within the applicable scope of a specific CE directive.