I don’t think the two things even belong in the same thought process.
Erecting a mosque near the 911 site would be roughly comparable to the Japanese buying land overlooking Pearl Harbor and erecting a gigantic “rising sun” flag overlooking the site. It would be comparable to some American erecting a gigantic 48-star American flag over the Hiroshima memorial in Japan. Maybe they would have a legal right to do it, but it’s just arrogant and insensitive to the legitimate feelings of others, and seems intentionally so. Is it sinful, then, to oppose the mosque? I can’t see that it could be, and it seems possibly sinful to favor it, since erecting it would be uncharitable in the extreme. There is nothing to prevent the Muslims from building a mosque elsewhere, just as there is nothing to prevent Japanese from putting up a gigantic flag somewhere other than at Pearl Harbor.
As to wearing the rosary around one’s neck, to my understanding, it is not considered proper from a strictly Catholic standpoint to do it. But it really has nothing to do with the religions of others and, to my knowledge, is not deemed arrogant or offensive to others. I don’t think the state has any place telling Catholics how they should practice their religion properly. In any event, for some it seems to be a cultural thing.
But as I said, there is no moral connection between the two things. At least not now. The time could come, of course, as in France, when the only way the state feels it can prevent
religious conflict is to ban the wearing of religious symbols altogether. It could come to that someday here. But it’s not today.