With my interpretation of 'rebirth', can I become a Buddhist and become accepted within a Buddhist community?
You don't have to believe in rebirth. Rebirth concept in Buddhism is not as simple as simple as reincarnation anyway.

It's actually better if you don't hold any blind beliefs in Buddhism since it is a find-out-for-yourself kind of religion, i.e. when you reach the proper stage you will have the insights.

It all starts from working on the trainings for morality, concentration and insight.