“Membre” est utilisé comme adjectif qui définit son statut par rapport au club.

You can very well say “Tu es membre de notre club.”
As you can say for example “Te voilà le chef de la famille.”

So I am not convinced that there is any difference in usage after “Te voila ..” and “Tu es ..”.

“Tu es membre de notre association” is used to indicate that you have the statute of a member.
It is more idiomatic than “tu es un membre de notre association.”
because the article is only used if you want to precise
what kind of member you are:
“Tu es un membre actif de notre association.”
“Tu es un jeune membre de notre association.”
“Tu es un membre blond de notre association.”
“Tu es un membre récent de notre association.”
Somehow, the accent is on the adjective (“actif”, “jeune”, etc.).

But if you want to precise the statute, the article comes back:
“Tu es membre honoraire de notre association.”
“Tu es ‘jeune membre’ de notre association.”
meaning that the association has some particular statute of “membre honoraire” or “jeune membre” for some of its members.