Cite only "good papers" or "all expected papers"?

In my discipline the typical structure of an article is introduction, theory, previous research, data/methods, results, conclusion. In the section "previous research" you describe the state of the art in your field regarding the research question from your article. As I understand the OP's question, there is a group the OP disagrees with, but who are considered in your field to be important. In that case you need to refer to them (not every single publication, but one or two main publications), even if you think their way of doing things is substandard. That does not mean you have to agree with them; you can tell your audience how your approach differs form theirs and how your approach is (in your opinion) better. But ignoring an important part of your field is bad. Addressing substandard practices is how your field can move forward.

Pragmatically, not citing them in the previous results section signals to the readers, editors, and reviewers that you are not aware of important parts of your discipline or that you don't want to take part in a particular debate. Both can easily lead to your article being considered less relevant, which could get your article rejected or ignored.

If they are always citing all of their own papers, a good solution might be to just cite the last one, "and references cited therein". If you cite a review, you're also not citing every publication that's mentioned in it, and you don't have to do that here. This saves you from clogging up your paper with crappy citations, and doesn't give them too many undeserved citations.

You also write that you don't want to make any big statements, but you can just write some facts if you want to make a point in a more subtle way. For example: "some models that were thoroughly calibrated validated are described in [good publications]. Models published by [weak group] show that ...(something else that's also relevant)". You could definitely write somewhere "models in [xxx] not used because code was not provided".