"If a Catholic wears a crucifix or a Jew a yarmulke, is that a "public declaration of faith?"

The yarmulke is, the crucifix, if it is a small jewelry on a chain around the neck, is ambiguous. Because the latter is often worn simply as jewelry, because people think it is pretty, by people who are not religious. I am tempted to do so myself, but refrain because I do believe it would be misleading as to my religious beliefs. Not everyone feels that way.

As long as it is small and discreet, I don't mind too much, but I admit it does bother me, because I don't think it is a good thing to conspicuously display your religious identity, whatever that is. Nuns and priests who display large crosses are of course doing so deliberately, it is their job.

It is a good thing we got away from that kind of sectarianism. It says, "I am not one of YOU,"  to anyone who does not share that identity. That is not conducive to harmonious social relations. Such sectarian identities are better muted imo.