... but I can't imagine that Federation Membership could be based on anything else. You can't base it on species, after all
Problem is ... that isn't what we saw. Amanda wasn't a Vulcan-woman, she was a Earth-woman, this is how her son referred to her. Amanda never became a "Vulcan," even though she (apparently) lived on Vulcan since before Spock's birth and was married to a Vulcan.
Deanna Troi's Human father was never referred to as a Betazed, even through he lived on the planet, and he was married to a Betazed.
There is no reason whatsoever to think that they are referring to their legal citizenship rather than culture.
So was Amanda represented in the Federation Council by the representative of her Human species, or the representative of world of her birth, or the representative of world she happen to be living on?
Well, let me put it this way:
I was born and raised in Ohio, and attended college in Ohio. I very much consider myself an Ohioan. I currently live in Maryland near the border and work in Washington, D.C. I still think of myself as an Ohioan, and find that Marylanders, Washingtonians, and Virginians are all kind of weird in their own unique ways. I doubt I'll ever fully acclimate to the East Coast, and I still refer to myself -- and am referred to by others -- as an Ohioan. This does not mean that I am not legally a citizen of the State of Maryland, or that I am not legally represented by the United States Senators and a Representative from the State of Maryland. I don't get to vote for a United States Senator from the State of Ohio this year, and I'm not represented in the Congress by a United States Senator for White People.
Amanda may be referred to as an Earth woman. She may well think of herself as person of Earth, first and foremost. She may well never fully acclimate to Vulcan culture and may never really think of herself as a Vulcan. None of that precludes her from obtaining Vulcan citizenship and being represented on the Federation Council by the Federation Councillor from the Confederacy of Vulcan (established in the novel DTI: Forgotten History
to be a Vulcan female named T'Nuri during TOS, who served as Chair of the Federation Council's science sub-council), and none of that indicates she gets to vote for the Federation Councillor from United Earth or that she is represented by a Federation Councillor for Human Federates.