I suspect their point is less about belittling you or issuing a chauvinistic smackdown than three variations on the “no true scotsman” fallacy.
If a person wrote “Christian” in their bio then proceeded to write something like “Blow them tea-towel wearing sand-n@$#&*@ up in Iraq cos its ‘eye for an eye’ in my Bible” we might expect a similar vein of criticism.
We might see people writing “If you are a Christian, which I doubt at this point, I would put you in a league with TV Evangelists. You chose the bits you like such as retribution but conveniently forget the bits you don’t like such as grace (just like TV evangelists only focus on the prosperity of the gospel not the sacrifice and suffering inherent in it.”
Or perhaps “If you really are a Christian, you should know that cherry-picking verses is always counter-productive. “Eye-for-an-eye” was a Jewish concept instituted to restrict the common barbarian acts of revenge killings and disproportionate force in retaliation. It was designed to constrain the wholesale slaughter of those who wrong you by introducing a concept of justice and proportion. Did not Jesus also say to “love thy neighbour”, and “love thy enemies”?
Or perhaps a critique like “I hope you’re not an evangelising Christian because you’re obviously not familiar with the concept of Micah 6:8 which extols the virtue and duty of “love(ing) mercy”.
Sorry if I’ve belaboured the point but I was trying to echo the exact same arguments you yourself quoted. I’d argue its more of a rhetorical flourish designed to suggest your points of view are out-of-whack or perhaps unconsidered. Naturally I can’t comment as to veracity of their or your arguments as the quotes don’t provide context.