As an Orthodox Jewish married woman, I cover my hair with a scarf, hat, or wig in the presence of any men other than my father, brother, husband (or theoretically grandfather or sons, I just don't have any!). Most married woman have 1-3 wigs depending on how often they plan to wear "hair" vs. scarves (daily, for the Sabbath, for special occasions, just for work, etc)- and almost every one of my "curly" friends has gone stick-straight!
I actually see a different side of the self-perceived "stigma":
I spent 20 years learning to love my hair, and refused to buy a straight wig- but some friends think the straight wigs are just "easier" to deal with. (Funny, because I care for my own wigs; they all send them to a stylist every few weeks for a $30 wash and set...).
In other circles, curly hair is considered unkempt and immodest- usually because of a cycle in which no one knows how to care for the hair, so they just brush it and yank it into a ponytail or braid, and it frizzes up like the kid stuck their finger in an electrical socket, and round and round we go! Once these kids grow up hearing about how their hair is so "messy" and "inappropriate", they all run at the chance to wear a straight wig!
Just for the record, the photos below are my hair and my wig.