Most synagogues do not check whether you are a member or not before you enter to daven. Entry to a shul is not based on membership. There are usually no tangible benefits, unlike dues to a symphony society where you receive tickets to concerts. And if you do not receive tickets, and your dues merely support the symphony, I must disagree with your statement on the tax deductability. Synagogue dues generally go to pay necessary expenses, which might answer Jonathan Robbins' question about why synagogues charge people to belong.
Someone has to pay the rent, heating, electricity bills, etc.
It might be nice to be idealistic and take the position that you shouldn't be charged to pray, and indeed, few shuls would ever try to keep out someone who was not a member, but the money to run the synagogues must come from somewhere.