I have faith in many things and in many concepts and views. I also believe in many things the same way. None of this has anything to do with organized religion which is not something I believe in. People continue to euate faith with organized religion and they are NOT one and the same. This may be where your conflict begins. I have no conflict being critical of faith because everyone I know myself included has faith in something. Everyone I know myself included believes in something. so....no conflict here.

I tell proselytizers that my granny taught me to never discuss sex, religion or politics in public. Of course, I do all of the above, just not with them.

Difficult question.
I generally don't discuss it much unless I already know the folks involved. Otherwise I tread lightly and try to read the other person's reactions or frame of mind.
If it's a simple chat where the topic comes up and there's no malice intended, I might casually mention that I'm 'not that religious' or some such non-confrontational comment. If they ask, I full on say I'm an atheist, but I respect their right to believe and leave it at that.
If the conversation was disrespectful or confrontational from the start, I tend to walk away. It's not worth the effort or stress of dealing wish jerks. If they are already in an aggressive frame of mind, a civil, calm discussion is probably not possible.
But that goes for any topic really... I don't like aggressive, confrontational jerks.
That may or may not answer your question.
I guess I'm only openly critical against someone else's beliefs if they attack mine.

Catnublia, You will not be able to not offend with everybody so don’t worry about it. Ridicule, contradiction and criticism are all fair game when defending your convictions and disputing some one elses. But, this can be done without personally insulting the person you disagree with. Be understanding and repeat their arguments back to them so they know you understand. Dispute what they say politely without getting personal. Question everything that is not documented by good evidence. Also remember they have the right to wrong.

We all have the right I suppose. But what matters is how you feel about it. And in regards to how someone else reacts. You could be nice in your approach with them and they'd still be offended. Because it's all about perception. If they perceive your discussion as an attack on their beliefs then regardless of your intent, they'll probably take offense. With faith we need to realize that most people have an emotion attached to it. In religion here, it's a family thing. Listen to sermon, be with family and friends, go out to eat afterwards some. It garners pleasant memories. So, when one sees what they perceive as an attack on their faith (real or imagined) they also see an attack on those memories and emotions. And emotion is what makes most people regardless of faith or lack of it irrational at times.

My dearest sister! Is this at all related to a certain religious professor of ours who has made remarks saying you're too aggressive and combative? Because you know his remarks are ignorant and absolute horse shit. However, if you're asking for opinions, I have some to share! There's nothing wrong with stating your opinion. Nothing wrong with pointing out something you think wrong, however, when you argue/debate with religious people you often present your point aggressively like an attack. Maybe that's where people get offended? I get what your trying to say when you say the stuff you do, but you're going to have a more difficult time convincing others when you appear to be assaulting their opinions...
Am I making any sense? I'm not saying to tolerate horse shit opinions, and of course correct people who are clearly wrong. But don't do it in a challenging way? People are easy to offend, and become extremely defensive when they think their truths and beliefs are attacked, so present your opinion as not an attack but something else. Even the weirdos we deal with in our day to day life should be more open to your opinions then! I think at least. I can't hope to predict what religious crazies will do.

I have no tolerance left for religious people.
There's no debate, no discussion.
My politeness is in direct proportion to their rudeness and persistence.
So I have no advice on it.
. The latest was a guy who walked up to me in a diner saying :
I have a job for you !
. Yeah ? What's that
...go to a bible and look up..
. Fuck off with that shit.
. If treating them such makes me an asshole, I'm ok with that.