My boyfriend doesn't answer his phone when he's out. Should I expect him to answer out of respect?

...not a good sign, imo

Can you give examples of what you've called him about before?

When you NEED him. Not just for a chat. If you're texting him all of time, you're essentially just making a real-life example of "the 'girl' who cried wolf". If you want him to answer more quickly, call him more rarely. I wouldn't answer my phone to my Girlfriend if she called me too much when I was with my friends. It gets annoying.

if it's an emergency, you could always text him with the specifics of the emergency.

Let's be honest, there really can't be that many occasions when you totally NEED to talk to him while he's out. I think you're probably being insecure and LOOK for reasons to call him (and probably call much more frequently than you admit to us and to yourself) and that is what annoys him and why he doesn't answer. Really, give him those few hours with his friends without trying to get in touch with him.

As for your worries about emergencies: you could always call someone else if there's an emergency. He isn't the only person on this planet.

Some people think its rude to answer calls in another company

Ok men are one track from my experience. When they out they out they will check their phone periodically but not by habit like we as women do. I always check my phone no matter where I am church, school, work, shopping, etc. Men not so much