I don’t understand exactly what you are asking. It would be helpful if you edited your post, so that it was more clear. It’s a little difficult to understand.

It reads as if you are saying that non-believer only pertains to Christianity. Is that correct?

No one knows how the universe actually started. Not even Krauss. Anyone who claims such knowledge is overdue for a long toilet sitting.

Agnostic: no knowledge of how it all began.

Anti-theist: there ain't no invisible, all powerful, assholes fucking with humans on this planet.

Well, at least that i "know" of.

I don't think a conciliatory approach is a concession. Civility and tact can sometimes be used to more effect then broadsiding with rhetoric. They may even agree with your heretical ways, without knowing it.

These discussions sound incredibly dull and anti-climactic, arguing over terminology and such. Why would you do that to yourself?

You're too old for that shit, Dave.

Perhaps... fuck off religion is fairly appropriate....

Religious theologians actually teach a false narrative about Atheism and Agnosticism. Your opening statement tells me many in that group are still laboring under that.

"the group took issue with my assessment stating that a “non-believer” is an atheist by definition."

This tells me they are viewing Agnosticism and Atheism as points on a linear line, on the left, Theism, In the middle Agnosticism, and on the right Atheism, this is FALSE and INTENTIONAL by theologians.

A-Theism is a response to Theism, the a prefix denotes "lack of"
This is a position on belief, you have a belief in a God, or you lack a belief in God

A-Gnosticism is a response to Gnosticism, the A-prefix denotes lack of
This is a position on Knowledge, you claim to have knowledge of a God, or you claim to lack such knowledge of a God

Religion does not want to even acknowledge Gnosticism, because by doing so they have to admit Atheism (a lack of belief) has weight.

With the FALSE linear model, they teach followers that Atheists are COUNTERCLAIMING, claiming that Theists claim there is a God, Agnostics do not know, and Atheists claim there is no God. That is wrong both on linguistics and basic honesty.

Non believers do not recognize any diety

I'm reasonably sure the boundaries between the catagories you are contemplating (atheist/agnositc/non-believer) are very fuzzy and always will be. People have different starting points and obviously often land somewhere in between. Some folks are raised in a religion some are not. How can they become non-believers if they never believed? Some try various religions looking for a fit. Some don't seek in that way at all.

You are wrong. A npn believer doesnt believe in any gods and any religions

You can be an Agnostic theist or an Agnostic atheist. Gnosticism is about knowledge that is all. Therefore you can be a theist but know if there is a god or you can be an Atheist and not know. The point is you can never prove a negative, as in I can't prove there aren't any unicorns or fairies etc I just don't believe there are such things. Same with gods etc.

If it's what you truly think concede nothing and hold your ground, let people think what they think because at the end of the day it really doesn't matter, be true to yourself and let them do the same.

I'd let him call himself a kangaroo if it made him feel better.

Perhaps he just likes to be one to stir the pot...and call himself an atheist at a church meeting, yet still has religious beliefs.

Or perhaps to some religious communities, non-christian gets conflated with atheism..."cuz if you don't believe in the one right god, then you don't believe in anything". This sounds like the scenario you are describing. I would consider trying to help them clarify, but...you also can't battle idiocy with logic... so...choose your battles accordingly.

No knowledge comes from arguing semantics. If someone resorts to semantics in an argument, it almost always means they are losing and just trying to change the subject.

Do whatever you feel like. Lots of people are radical regardless of belief. As for me, I'm an agnostic atheist.

Everybody is looking for a label! Who cares? State yer opinion & carry on with the conversation.
Never concede your position, unless it is negated by the evidence.

Never concede.
You are entitled to your positions and have every right to defend them.
There's nothing wrong with challenging the false assertions of thumpers. Especially since the bible is only fiction and not a reference book. They don't get to quote it like it's fact.
Stick to your guns.