People where I am from call everyone "you guys" - men, women, trans, doesn't matter, everyone is just "you guys" even when it's a woman addressing a group of women.
The literal meaning isn't gender neutral, but in actual practice, it 100% is.
As for "y'all" or "you all", I don't see how it could possibly be interpreted as offensive to any gender.
Dude is also situationally gender neutral. Saying "Hey dude" to a trans woman is misgendering her but exclaiming "Yo dude check this out!" or "Duuuude no way" is perfectly acceptable.
Literally the entire rest of the sentence is the problematic part. "We don't take kindly to you", it doesn't matter if they say "y'all", "you all", "you people", "your kind", take your pick, it's not the problem with the sentence
I don't see the issue with using the term "guys" in the plural when referring to a group regardless of sex. That would align with the definition of the word. I'm pretty sure that's how they meant it.
Unless you can ask a straight man how many guys he’s slept with, it isn’t gender neutral, no matter how resistant to this fact you are.
E: the fact that neither of you give a shit about the people telling you the term isn't gender neutral, doesn't apply to us, and that we don't feel comfortable with you using it to speak to or about us says it all. No matter how much mental gymnastics you do to convince yourself otherwise you are the ones choosing to be the problem instead of actually listening to others and showing some basic respect. It's an easy fix, too - all you have to do is give a minimal fuck about others.
don’t feel comfortable with you using it to speak to or about us
This actually is relevant, but wasn't part of your initial statement. If you don't like people using the term to refer to you then people should absolutely make an effort to not use that term when referencing you.
Saying there's some mental gymnastics on my part is a bit of stretch, it's how the word is defined in the dictionary. All I needed was to read. There's no disrespect here, if you don't like it then using the term to refer to you would be disrespectful, but I haven't done so.
That's how people use it, whether you like it or not. I did not invent the language, but that's how people use it.
Saying "guys" on its own is also not the same thing as "you guys" in regions that do this.
You can shoot the messenger all you like but it is what it is and I have no power over how people in a region use a language, I am merely informing you of that fact.