And yet, novels aren't canon.
No, but when a novel states something (in this case, "Trill is a member"), and there is nothing in canon that explicitly contradicts it, then it still counts in favor of the premise being discussed.
For that matter, the Federation can have ambassadors from non-member worlds.
Think of it as being akin to ties between the Federation and non-member worlds being strong... they have a number of agreements, excellent relations, except, they aren't a member.
Not really, no.
We're talking about a Federation Ambassador, meaning, one who would engage in negotiations on behalf of the Federation. Expecting non-members to conduct these kinds of negotiations properly is ludicrous. "Excellent relations" is still not at all the same as "you are part of our society".
For an individual to attain such a position, despite their species not being members, would mean that the individual had become a UFP citizen for some reason, early in life, and had worked within Federation diplomatic circles for quite some time. Their ties to their original homeworld would be comparatively minimal; they would have had to truly throw themselves in to their life as a UFP citizen and public servant, and they certainly wouldn't be able to maintain a highly visible profile as a representative of their original, non-member, species.
This does not describe Curzon. He was an extremely skilled Federation ambassador, AND a well-known (nigh unto legendary) figure
as a Trill and host of the Dax symbiont. These various aspects of his life are all core to his character.
Trill is a member.
I see no reason why Bolians or Trills would be UFP members.
Strange sort of "in favor of the negative" wording you are using here.
What, exactly, is the reason why they SHOULDN'T be members?
It's possible they are non-members and yet have numerous people working in SF of their own choosing.
Absolutely. The Bolians and Trill needn't even be brought up when addressing this specific point: Klingons, Ferengi, and Bajorans are sufficient to demonstrate that individuals from non-member species can join Starfleet, as there is NO room for debate that those three species are not members during the shows. But being an ambassador is a whole different matter.
As if people today from other countries aren't living in other countries (which are not of their origins) and are in high-ranking positions.
Wait... what? Who is living where and is from where (or isn't)? This sentence is all over the map (no pun intended).
And, "high ranking positions" doing
what, exactly? Obviously a country's government works with a variety of individuals, both from the country in question and from others, during day-to-day foreign affairs operations. But to be an ambassador
representing the interests of a nation, you have to be
from that nation. For Curzon be a Federation ambassador if Trill is not a member, representing the UFP in key early negotiations with the Klingons, would be like a man living in France, who has visited the US many times but was born and raised in France, becoming the US ambassador to China.
Excepting, as I outlined above, an instance where someone who is
biologically not from a member world, but gained individual UFP citizenship and worked their way up to such an important position. But again, that's clearly not the case with Curzon.
The next Star Trek series should really just list all the Federation members so that we can finally have defintive word on who is or isn't a member.
Well, the reason they don't do that is to leave the door open for future writers who want to create another Federation race - one that is new to the audience, but has "been there all along" in-universe.
- because they personally will be affected by how they conduct their business on behalf of their government. 
