It depends what you mean by 'should'. If you choose to practice tithing, then it should be ten percent of your gross income, otherwise you are honouring the government above God by paying Caesar's protion first.
You may choose not to tithe because Christians are not under the law and may tithe or not freely. Galatians 3:10 & 13 says:
For as many as are out of works of the Law, these are under a curse; for it is written, "Cursed is everyone who does not continue in all things which are written in the Book of the Law, to do them...Christ redeemed us from the curse of the Law, being made a curse for us (for it is written, "Cursed is everyone having been hanged on a tree").
This freedom from the curse includes the curse mentioned in Malachi 3:9 against those who failed to tithe under the Law.
Nevertheless, tithing both pre-dates the law by several centuries and continued under the New Covenant as evidenced in Hebrews 7:5-9.
'And truly they who are of the sons of Levi, who receive the office of the priest, have a commandment to take tithes of the people according to the Law, that is, from their brothers, though they come out of the loins of Abraham. But he whose descent is not counted from them received tithes from Abraham and blessed him who had the promises. And without all contradiction the lesser is blessed by the better. And here men who die receive tithes; but there he receives them, of whom it is witnessed that he lives. And if I may say so, Levi, also, who receives tithes, paid tithes in Abraham.
Offerings are strictly speaking anything that isn't a tithe, and may vary as the believer feels led by the Spirit to give.
If a believer does not choose to tithe he is free to so choose, but he might like to consider Jesus' advice in Luke 16:10-11.
'He who is faithful in the least is also faithful in much. And he who is unjust in the least is also unjust in much. Therefore if you have not been faithful in the unrighteous mammon, who will entrust the true riches to you?'
We can't buy God's grace, earn his favour or pay for his love, but here he tells us that we can earn his trust.
If non-tithing is a principalled position based on a limited understanding of the Bible, that's fine by God who looks on the heart. But if it's just an excuse for stingyness (which Jesus calls an 'evil eye') then look out.