There are always going to be people in your life that irritate, annoy, and baffle you as to why they do and say the things they do. Sometimes you want to snap back at them about how pestering they are, or ignore them because you don't particularly like them, but remember, you have to be considerate of how that person feels and why they do and say certain things. Before you can judge, you need to understand that person's feelings and thoughts.
Before you judge them, step into their shoes. This is especially important. Maybe this person is constantly sitting by his/her self and doesn't like to talk to others. Maybe this person is cold to you when you talk to them or says things that might seem a little rude. Before you judge them and label them, think about how he/she feels—"Maybe s/he is always by him/her self because s/he doesn't feel comfortable around others. Maybe s/he isn't used to talking to people so s/he is a little cold. Maybe s/he wasn't feeling well on the day I talked to him/her and that's why s/he seemed to be in a bad mood." Before you allow yourself to label this person, imagine why they act or say the things they do.
Think about how you'd feel if you were treated the way you may treat this other person. It is necessary to think about this before you say something to another person. How would you feel if someone you weren't familiar with came up to you and said something mean to you, just because you looked/sounded/acted differently from what they expected or thought you should have? You would be pretty hurt, wouldn't you? Don't put someone through that kind of pain if you wouldn't want to be put through it yourself.
Don't let one encounter ruin your perception of that person. Just because someone seemed to be in a bad mood when you talked to them doesn't mean they are constantly angry and depressed. Maybe they were having a bad day when you talked to them, or they weren't feeling well. Try to speak to them more often and see how they act; don't let one time ruin how you see that person. You have to be around them frequently to see how they really are.
When you talk to them, don't let your insecurities or beliefs get in the way. It's very common to meet people with different beliefs, likes and dislikes than you, so don't be put-off if the person you're talking to doesn't like something you do, or likes something you do not. Don't let their belief in God (or no God) make you feel any different about them. Remember, being sensitive to their feelings means accepting what they like/dislike and who/what they believe in. It's how they feel for a reason, and you should respect that.
When you start to feel irritated, stop yourself from saying anything. Think to yourself that there is a reason this person is acting the way s/he is acting, and that you should respect how they feel at the moment, even if it bothers you.