Not usually. Though from time to time I remember a post (here, maybe) from someone that worked in a clothing store. They said that when the trucks unloaded all the racks of clothing, they’d have to leave them in the back room for a day to air out and get rid of (what they described as) a formaldehyde smell. I assume it’s just whatever the final rinse was after making/dying the clothes, but it did get me washing new stuff for a while.
ETA, I believe this is the post I was looking for:
Plus, I found lots of other posts about formaldehyde being used in manufacturing process (including one from Lynn).