I don't recall "Attached" establishing anything other than that the Federation doesn't usually accept as Members states that do not have universal jurisdiction over their home planets.
I remember now, it's DS9's "Accession" which states that the Federation forbids caste based discrimination. Those two are really the only universal laws that all members must abide by, that I'm aware of.
They're the only two have have been canonically established; this does not mean there are not more.
Further, we know from TNG's "The Drumhead" and VOY's "Author, Author" that there's a provision of the Federation Constitution/Charter called the Guarantees. There are at least twelve of them. The Seventh Guarantee protects all sentient entities from giving self-incriminating testimony during a trial or hearing (in other words, is analogous to the Fifth Amendment) ("The Drumhead"), whilst the Twelfth Guarantee defines an artist as a person who creates a work of art ("Author, Author").
We know from "The Perfect Mate" that any sentient entity aboard a Federation starship is entitled to all of the protections of the Federation Constitution. The implication from "The Drumhead" seems to be that the Guarantees enumerate and protect all Federation citizens and all sentient entities in the territory of or in the custody of the Federation government.
Still, we do not
know this for certain. If we accept the idea that the only two rules the Member States must obey are no caste-based discrimination and keep a unified government, this presents the possibility that a Member State government might force a suspect to give self-incriminating testimony, or violate any number of the other Guarantees, and it would be totally legit -- just like how the rights conferred by the US Constitution were regarded as being legal for state governments to circumvent until the advent of the 14th Amendment.
So, ultimately, that's the question: Does the Federation Constitution, or Charter, or the Articles of the Federation, or whatever you want to call it, have an equivalent of the 14th Amendment? Something that says that the rights enumerated and protected by Federation law override attempts to violate them at the Member State level? Something that says the Federation government can overrule local law if there's a conflict? Or do Member States have what the South Carolinians believed they had in the 1820s -- the right of nullification?
We don't really know, because the issue has never come up canonically.