Yeah, I also feel embarrassed when I see people praying in public...
If they look weak or undereducated I'll pretend not to notice. A bit like ignoring it when someone's farting in the elevator in order to spare them further humiliation.

But if they are in a position of authority, I will debate them as I will any other accountable person promoting unethical ideologies.
Before you ask what the unethical part is, a perfect illustration runs through this thread: confronted with explicitly religious motivated crimes, some believers still choose to blame the mysterious immorality of single persons in order to protect the powerful moralist doctrine itself from criticism.
But thing is,
every set of ideas is invented, carried and promoted by persons. And just as persons can't be reduced to an idea, ideas cannot be reduced to persons. Using people as default scapegoats to divert criticism of a corrupt doctrine simply will not do. People cannot be used as a lazy free-pass, pretending that bad ideas have nothing to do with the actions of their followers. Ideas
do influence collective perceptions and actions. Human intelligence will be wise to make them the object of critique.
The ethical standpoint being of course that it's people who should be protected (religious people included), not their ideas. Ideas must be challenged and scrutinized, never made sacred.
Oh, and defending
religion by accusing secular humanism and critical reasoning for bigotry seems... cynical. Could be funny I guess, if superstitious belief weren't still wrecking havock around the world.
But, hell, we can take it.

(Laurie Anderson: ...and if we can't, we can fake it...

)