I'm not adding any additional meaning. As I explained, nobody says, "My group is above criticism" but what they say is, "The criticisms against my group are nonfactual and/or disrespectful." Everyone agrees with the principle you've said, but that principle is completely meaningless because any perspective that wants to shut down criticism will just say that it's nonfactual or disrespectful.
If you just think critically about it and break down what your statement actually means, it's just "I agree with criticism I agree with." I don't really know what more I can say to explain that, it seems very straightforward to me. From your other comments, you talk about people criticizing major religions, well, suppose someone from a major religion says, "I agree, and also, I think such and such criticism is disrespectful." Maybe you don't think it's disrespectful. Maybe they make a criticism about you that they don't find disrespectful, but you do. Who determines which criticisms meet the criteria of factual and respectful? Everyone can accept your standard and carry on exactly as they were, simply saying that the criticism they agree with meet the standard and the criticisms they disagree with don't. It's pretty meaningless.
Are you often finding yourself in situations where people aren't disputing facts and norms, but just whether, in principle, legitimate criticism should be said at all? Can you give me an example?