I have been doing it for decades to canvas, vinyl, nylon, dacron tents,
sails, awnings, boat covers, Bimini tops, etc., etc., etc.. I always
rinse good with a strong hose spray and have never seen evidence of
thread degradation. If diluted household bleach attacked some thread,
then it would also attack some fabrics and a lot of our white clothes
would fall apart. It's just not that strong after almost any dilution
with water. I suspect the hat manufacturer is more concerned with the
color of the thread changing so it didn't match the fabric. My concern
with bleach is with metal which is why I now try the oxyclean stuff
first (it still needs to be rinsed off good).

Now if you go to the pool store and get some pool bleach and pour it all
over your vinyl seats and it gets down in the metal hardware, then
that's another story, but I trust we all know not to do that.

Ron