Traditionally, this is because Jews are not permitted to carry money on Holy days and Shabbat. There are two primary approaches to synagogue dues. Some congregations set a fixed fee based on membership categories. People are not turned away because of ability to pray. It is important to note, however, that you do not have to be a member of a synagogue in order to worship there.
Synagogues are, for the most part, independent community organizations.
Individual synagogues do not answer to any central authority.