Your point is a bit skewed. You seem to constantly take the stance of religion being this benign thing that if you leave it alone it will leave you alone.
No I don't. If you befriend religious people who hold opposite views than you on a particular subject, you can easily persuade them that they are over exaggerating, thus you can make them step down and even support your own cause. It's a fact, people hate being told that they are wrong. Tell a Christian that his heart is in the right place and that his morals are gold, and he will likely begin to agree with you when you say "welll, homosexuals aren't that bad. Sure, it's gross (you may have to lie some), but they aren't causing anyone any harm. God will judge them in heaven." If that's enough to make them stop their anti-gay activities, then I could care less if they believe in God or not. I could care less if they are using proper logic or not.
3. teach the person how to use critical thinking skills improving there ability to reason. Just as a teacher in school this sometime requires pointing out clear errors.
How do you suppose we do that? We teach them how to critically think by teaching them God doesn't exist.?
If there's anything you should know by now, it's that people learn when they want to learn. Why do you think teachers repeat themselves in class so much? Because when they have a class full of students who don't want to be there, they must say something over and over until the students remember the repeated phrase.
When you're in a debate, you will often find people aren't there to learn. They are there to get their point across. They don't want to be told that they are wrong. They don't want you to teach them anything. They want you to side with them. That is why it's VERY important not to tell those people that God doesn't exist. As soon as you do, they put up a shield and they stop listening. It is human psychology.
People will believe what they want to believe. You fail to realize that
not everybody seeks knowledge like you do. Most people seek comfort. If there's one thing most churches offer, it's comfort. I can smoke a joint or a cigarette to calm me down. I can drink my troubles away. Some people enjoy going to church to releave them of their stress.
So when asked the question why we care it is not a question of why we care about those not pushing there beliefs in any way on others but why we care about those who are and those who allow it to happen.
If the problem is, as you say, people forcing their religious views on you, then there is an easy solution. If someone asks you to believe in God, simply say "no thanks." Most people out there will drop the topic when you politely say "no." If not, you can figure it out without having to go on a mission to abolish all theism.
If the problem is religious influence on politics, then you have to challenge it one way or another, and that's where I come in to explain that there are better ways to solve problems than to simply persuade people that God doesn't exist. If it's the religious influence on politics that are bothering you, then you need to figure out a way to persuade those people that their God doesn't want them doing whatever it is they are doing.
If you simply look down on people for thinking illogically, then, I don't know what to tell you. I think you would be better off spending your time picking at the stupidity of star struck people and the illogical behaviors of everyone than just theists.
Why try to persuade everyone that they are wrong when you can push for coexistence?