Christians should have every right to tithe if they wish to do so. Giving back is part of their religion, so if they want to help, then nobody should be able to tell them otherwise. Furthermore, I think it's a silly idea if they were prohibited of doing so. This should be a right for them.
Yes, Christians should tithe. Churches depend on the generosity and donations of their congregation to survive and grow. True Christians are morally bound to tithe at least ten percent of their income to their church as confirmation of their faith. As churches are non-profit organizations, they would be hurting financially if their members did not tithe.
For as closely as most Christians claim to follow the Bible, then technically they should be taking a tenth of their income and giving it over to the church. Although I personally am not religious, I do expect people to "put up or shut up" when it comes to following the rules of the religion they claim to adhere to.
If you have not put your sinful nature to death, you are still under the law, and tithing is still relevant. If you want to be judged under the old covenant rather than the new covenant, keep believing in tithing. If you want to experience freedom in giving and true stewardship, obey how much the Holy Spirit tells you to give, and where he tells you to give. Should the church teach tithing? No. We should be ministers of the new covenant.
Christians are to give freely, as they are prospered, and not a certain percentage - a tax of 10% - as imposed under the Mosaic Law. One will search the New Testament in vain for any instructions for Christians to tithe. Tithing is thus simply a hold-over from Judaism as are animal sacrifices and burning incense.
Each individual needs to decide what they can and can't afford to give to charity, be it their church or other worthy organizations, but they should not be required to give 10% of their gross earnings to any one church. There are so many valuable charities and unfortunately, poorly run churches, that a person should be able to decide to whom they want their hard earned money to go.