"I adhere to Buddhism; I am Buddhist; I am a Buddhist." The answer to "What religion are you?" is "I am Buddhist" or "Buddhism is my religion."
The 'a' is optional in many cases, eg. I am Australian; I am an Australian. It doesn't matter.
The names of religions are very, very often mangled. Christian isn't technically a religion, Christianty is. Muslim isn't a religion; Islam is.
Jewish is not; Judaism is. However, the adjective is usually given to the simple question, "What religion are you?"; "Buddhist". This is OK. But it's wrong to say "My religion is Buddhist".
Student or Learner