I'm curious, what "New Atheism" thing that you don't agree with, that when you told them about it they think that it's because you're still brainwashed?
"Brainwashing" is just a label, technically we are all brainwashed at something. Even the most rational person would still have something they follow blindly... Atheists from secular country will have different ideas compared to atheists from Catholic countries / Islamic countries.
Usually, for me I think about the matter a lot and think about the reasons (actual reasons, with facts backing it up) why I feel that way. If you actually have facts backing your opinion, then you shouldn't feel like you're being brainwashed. In discussion, bring up the facts.
I am talking about those who simply regurgitate what they have read in a book written by Sam Harris, Christopher Hitchens or whichever other Anti-theist they like to quote. It's one thing to admire someone and agree with them most of the time, it's another to take everything that they say as gospel. The same way that some Muslims have the mentality of "if you say XYZ, it means that you're religious", that have the mentality that "if you say XYZ, it means that you're smart".
They are forever patting each other on the back for realising that religion is nonsense. OK, so you know that it's all indoctrination, good for you. It doesn't mean that everyone else is stupid and that you are necessarily more intelligent than the average person, especially since you have joined another religion without even realising it. (sorry for the rant
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The comparison that you made between Atheists in secular countries and those in Islamic/Catholic countries is true. I have found a lot more mutual understanding between myself and the latter as opposed to the former. I guess that the way they view things is much less simplistic, since they were raised surrounded by religious indoctrination. However, there are still quite a few Atheists in secular countries who are not New Atheists.
We are all brainwashed in one way or another, but certain people will acknowledge this and work on educating themselves while others will not.