It is a fact, that if I see you visibly and publicly accessorizing with overt religious symbols, I will not respect you.
I will, of course, accord you the bare minimum of decent civilised back-and-forth, if I have to. That is, I will not fly into a secular rage (believe me, there is such a thing), draw my scimitar and chop off your head. But I will label you an idiot in my mind, and of course, you will be able to tell that from my eyes, the tone of my voice, and the angle of my nose.
It is not just the fact of you wearing a headscarf or a cross or a skullcap when you are not literally forced to do so that will provoke my disdain. Even small, online declarations of faith are tantamount to publicly stripping and running round a black rock seven times. For example, if we are corresponding via e-mail about some general daily matter, and I notice your profile pic is a cross and rosary beads, then you immediately slide into gibbering idiocy, as far as I’m concerned. After all, in this day and age, and with all that has happened and is happening, you still have the enormous stupidity to think it is cool or desirable to publicly announce your allegiance to some supernatural, incendiary faith or other, then you are stupid. Let it be said.