It doesn't bother me. People know I'm not religious. And they're not really praying if they're giving you look and questions. If you're really worried about it, pretend that you were praying too when they look up. Lmao.

Can't say I hate it, I actually have never given it any thought, which is what it's worth to me.

Nobody has ever said diddly squat about it to me.

Being in healthcare at an xian based hospital I find myself around much more prayer then I would like. But since taking care of pets involved trying to meet spiritual needs to I go with the flow. Or try to not be near when it happens.
When I worked at the VA they made a pretty big deal about having sexular/athiest chaplains avail ro patients

I don't understand what the big deal is. I usually bow my head in deference to the intention of the prayer even though I don't believe the God references. It is also polite to do what custom dictates in a given situation.

I stand quietly with eyes open, chin up, sometimes looking around, and at times checking out the ceiling.

You get used to it.

Well if they judge while they pray Santa won't grant there wish.

I stand there and look around.

Just look at the food cooling on the table and think how much better it would taste if some moron wasn't rambling on about nothing while doing a disservice to the person who cooked the meal.

I love it, not bowing. You get to look around and see if anyone may be cool there.

It does annoy me that I am NEVER asked if I'm ok with it. It's always assumed, you are. The religious have a default 'right' to inflict their crap onto you. Years ago, when my kids were in grade school, my then wife and I went to the school to complain that participation in the Christmas and songs, etc. was mandatory, and thus, my kids were required by a public school to sing religious songs. We were willing to compromise, asking only the pure religious songs be cut out. Santa Clause and snowmen were fine. You should have seen their faces.... This was a small community, maybe several hundred at most. Everyone knew everyone. This is why I started taking the kids to Unitarian church... they were always being pestered why don't we ever see you in church xyz? We DO go to church, was the response. Unitarian. Since no one knows what the hell a Unitarian is, that usually shut them up. I can be an atheist and a good Unitarian and NOT be a hypocrite .

I just look straight ahead while others are bowing their heads and make no comment

It's always awkward for me as well. I never close my eyes but I generally just bow my head to avoid any kind of confrontation.

Of course not. Check your fingernails. Check your shoes.

I just observe a moment of silence and allow everyone to have their moment of prayer. The hope is mutual respect but I do feel as though I am judged for not participating.

I don't think I've ever been to a public gathering where there's need to bow my head. If there was or ever will be, I'm certain I wouldn't be the only one.
Also - if they have bowed their heads, how can they see that you didn't?
In private gatherings (specifically funerals) I might consider bowing my head (or whatever the tradition might be) out of respect. In the same way that I would take off my shoes, or wear a head covering if asked, when entering any given house of worship. If I'm there at all, I'm there for a reason and I'll respect the traditions.
Respect doesn't mean I agree or believe.

Can't say I hate it, I actually have never given it any thought, which is what it's worth to me.

I never bow my head. I always look the minister (or whoever is praying) in the eye.

I understand that quite well. I go between just lowering my head, keeping my eyes open and peeking about to see if anyone else is doing it. I know that appears to be dishonest, but I really do not feel I need to insult a group of believers. It is difficult.

I feel really awkward when asked to peay

If I am in a situation where that happens I probably know going in that I would be (funeral, wedding, Aunt Barbara's for dinner)...So I have no issues...usually just look down and wait...on the other hand, if I was not expecting it and it was thrown on me I would have issues...

Fortunately, public prayer is very rare where I live.

Not really, Ma n Pa never cared. I'll hold hands when they say grace but they've busted me making faces too. Sometimes, mommy even joins in.

Some weddings and funerals have prayers and im good w a bit of reverence towards marriage and death

Yup. I feel tremendously awkward in that situation. Happens a lot too since I'm the only one in my family who is not religious. My family often not only wants to bow heads but also hold hands around the table before a meal in a restaurant which really weirds me out.