It is secular law that mediates our interactions. Consider this, which of these (if any) are ok due to religious considerations?

A public bus driver denies a gay rider. A public teacher will not teach a gay student. A police officer does not respond to a gay victim. A heart surgeon does not perform surgery on a gay patient. A public defense attorney does not defend a gay client.

Or, if religious considerations are justification over secular law, which ones?

Should a Mormon be able to have multiple wives? Should a man be able to take a child bride? Should a religion that embraces gays be able to marry them? Should a raped woman be stoned as in sharia law? Should an adulterous wife be killed as the Old Testament suggests? Should a muslim woman be able to remain veiled in a photo ID?

Where do our 'secular sensibilities' override our religious ones, and why?

I do personally believe that secular law should override religious law (and belief), when it regards the rights and welfare of others, our civil interactions. In that sense, yes, I think the secular mindset takes precedence. Not necessarily because it is right, but because it is the one that remains when specific religious beliefs, and secular ethics, are generalized into a Golden Rule type of civil society. It's the best place to agree to disagree.

Of course, I do not think it is always easy to separate the two, but I am not afraid of a slippery slope here.