Personally I don’t like the use of “evangelical” and “atheist” together, but I didn’t coin the phrase and people will say what they want to say. Of course, I don’t go around calling myself an “evangelical Christian” either. I simply use Christian or Baptist.
I tried to do a little surfing to find the term to see what I could come up with. The reason is because it is most often heard from atheists that they want Christians to keep religion to the church, their homes, and themselves and to reframe from proselytizing (their word). So I found the term “evangelical atheist” interesting because in it carries the meaning that they are indeed atheists which go about to proselytize/convert theists to atheists; which would go against what atheists are telling Christians to stop doing.
Here is the article and a small bit from it:
None of this means, however, that there aren't some atheists who really do want to convert theists. What everyone must remember is that this does not indicate that such atheists are just trying to convince themselves. There are many Christian evangelists who spread all over the world to convert people to Christianity, but are they all trying to convince themselves as well? I doubt many Christians would accept such a conclusion, but if so then they shouldn’t claim that it's true about atheists.In fact, some atheists think that theism, or at least religion, causes a great deal of harm in society, so they try to get people to change their minds. This isn't much different from someone having strong political convictions and trying to get others to change their minds and agree with them. An advocate for laws against abortion or gun control isn't trying to simply "convince themselves" — they are, instead, trying to improve society by promoting particular ideas and/or arguing against others. An evangelical atheist who argues against theism and/or religion is doing much the same.
So two things:
1] Before atheists scream at the Christian for obeying the Word of God and witnessing to every creature, please call off your own from witnessing that God does not exist; or simply except both exist and when a Christian knocks on your door simply say I am not interested.
2] As a Christian take into account that some people may not want to hear the gospel message. I am not saying don’t witness, I am saying when they say they are not interested, don’t cram it down their throats. We don’t convert people, God does, we simple present the gospel message to those that may accept or reject it.