Using radar gives away your position and radar capabilities. For this reason, most active navigation measures are (almost) never used on naval ships.

My understanding[0] is that use of radar to provide continuous situational awareness is routine, not avoided in the way you describe.

[0] confirmed by this piece by a recent US destroyer commander: https://warontherocks.com/2017/06/how-could-this-happen-the-...

And colliding with a tanker and being in the media for several days doesn't reveal your position?

I really get your point about stealth and would agree that it would make sense not to use radar. On the other hand, if you can't avoid collisions (for whatever reasons) your position will be known very quickly anyway.

Good point. Does this apply even in peacetime while in friendly waters? I suppose you never know when you might become a target.

Peace can turn into war very quickly indeed, so my understanding is that the Navy prefers to err on the side of caution.

Please tell me how a radar switched to off would give away the position of the ship in a war time situation.

You're sailing through the Strait of Hormuz, one of the busiest shipping channels in the world. There isn't a shooting war underway, but you are within range of Iranian cruise missiles and naval craft.

It's not exactly war, but it isn't exactly peace. Do you see what I'm driving at?

Huh? They're explaining why they wouldn't switch the radar on.