Can I take my dog out of the bag on the airplane?

I travel with my dog and I always feel bad how she has to sit inside her bag under a cramped space for 5 hours. I notice some people let their dogs out of their bags, and the crewmembers don't chastise them even though they aren't special service dogs. How do they do that? I just had the bag slightly open once and the crewmembers got all over me on that.