Imanonov said:
As such this person is a Tzaddik for putting himself in such an embarrassing situation for the sake of Halocho. At the same time it is definitely not a Chilul HaShem, because following Halocho is never a Chilul, but rather a Kiddush, HaShem. If you feel uncomfortable with that, you are suffering from a Golus mentality and need to improve your hashkofos (and knowledge of Halocho).
I respond:
Mesillas Yeshorim writes that one must not observe a Midas Chasidus if the Hamon Am will mock him. If there are shitos that mean the plastic big is unnecessary, it would appear that doing so is not really a Halacha but a Midas Chasidus, and would therefore be discouraged.
A Dayan in London wrote a very detailed comprehensive Teshuvah on the subject about 8-10 yrs ago, including all the points raised abvoe by various commenters, and concluded that the plastic bag would be a Chumrah but not required Al Pi Halacha. I believe the Teshuvah was printed in Techumin/ Kol Hatorah or some similar journal. If anyone wants I could look for a copy.