It sounds to me like the leadership in your particular church is imposing requirements on its members that are not biblical. For starters, there is no Bible requirement that prohibits the drinking of wine. In fact, if it is a sin, how is it that Christ's first miracle was the turn wine into water at the wedding? The other evening I was reading the Bible, and came across a verse in which Paul was encouraging the recipient of the letter to drink a little wine for the sake of his stomach. Our whole belief in Christ and His salvation is based on His sinless life. If it was a sin to drink wine, then He would have caused everyone who drank of the wine he created to sin. Not possible.
Regarding the tithe: Tithing is encouraged in the Bible, Nowhere have I read that it is a requirement. In fact, check out Acts 5:1 regarding Ananias and wife. They sold some property and decided to keep part of the proceeds. They lied about how much they had received. Peter said it was their money and they could have kept it, or given part as they saw fit. Their sin was not in giving what they chose to the church, their sin was in lying about it.
I once had an interesting conversation with our pastor's wife regarding playing cards and drinking wine. She stated that both were sins and therefor were prohibited. I asked why Christ's first miracle was to create wine if it was a sin to drink it. She said it led to drinking too much and that could lead to sin. I also pointed out that the Bible recommended drinking a little wine, but not to excess. She had no answer. (A/G church)
Regarding playing cards, her position was that doing so was a sin because the Roman soldiers had gambled for Christ's cloak as He was hanging on the cross. Nothing in the Bible about gambling or playing cards. In fact, many times in the Old Testament, the leaders of Israel "cast lots" to make decisions. I assume this was on the basis that God controlled the dice (or whatever they were using) to have them reach the decision He wanted.
In closing, I would not sign a promise that I would tithe, or that I would not drink wine. If they decide that you cannot join the church because you refuse to agree to something that is not biblical, then you should look elsewhere. If you like the A/G church find another congregation and see if they have the same restrictions. I would be very surprised if they did. This sounds like some of the "elders" are putting their own spin on things, and that seldom leads to "good things".
Fred