Why did Maria get angry when Chris told her he was a cop?

I would assume she felt betrayed because she was lied to. She might have felt that she was just used and taken advantage of.....

Because he had been lying to her and spying on her during the stakeout. She thought he was a completely different person. It was a betrayal of trust. If not for the life or death situation with Stick Montgomery, they never would have ended up together.

The same way you would get angry if you go to your dentist, and after having done work on your teeth he tells you he's not really a dentist, but a tv-repair guy.
It's a betrayal of trust. He just had his hands inside your mouth and was drilling your teeth, and he's not who he says he is - it doesn't matter wether or not he did a good job, he's lying to you while you are in a disadvantaged position.

She had recently fallen in love with "Bill" and they made love, and now he tells her he's not "Bill", he doesn't work for the phone company and he was never "just in the neighborhood". I doesn't matter what he says he is and does in reality, because all that matters is that he was lying to her.
Had I been her I would have punched him in the face so hard he wouldn't have remembered his own birthday when he woke up.