1, If it is common for people to wear masks, one is certainly allowed to wear a mask when there is no eruv (it is considered a garment, not something you are carrying).
2. If the goyim are uncomfortable see Jews who aren’t wearing a funky hat or a yellow star (and assuming going out in public doesn’t raise the danger of coming to harm from the goyim), are you allowed/required to do so. Does it apply if the government basis this requirement that Jews wear special clothing as health reasons, based on their own junk science (as was the case in Germany in the mid-20th century, where their science of eugenics held that it was necessary to treat Jews as a special threat to society – and note, that science was also the basis of anti-Jewish, anti-Catholic and especially anti-Black laws in the USA).