"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.