Matt 23:23 "Woe to you, teachers of the law and Pharisees, you hypocrites! You give a tenth of your spices-mint, dill and cummin. But you have neglected the more important matters of the law-justice, mercy and faithfulness. You should have practiced the latter, without neglecting the former. NIV

Jesus lived as a Jew under the Law, and taught Jews living under the Law -- and he explicitly related the teaching in Matt. 23:23 to the law, which the Pharisees and teachers of the law were bound to keep at that time. The teaching has to be taken in context, who Jesus was talking to is important, and when he taught it is important. Likewise, in Matt 5:23-24 Jesus teaches about presenting an offering at the altar. Christians don't offer sacrifices in the temple in the Jewish way, the teaching has to be understood in context, when Jesus said it and to whom he was speaking. Jesus has fulfilled the law, he came to do so (Matt 5:17, Gal 3:24-25 for example), including both tithing and offerings at the altar. But the principle of doing the details and following the big principles still applies, as does the principle of reconciling with your brother before trying to please God.

Matt 5:23-24 23 "Therefore, if you are offering your gift at the altar and there remember that your brother has something against you, 24 leave your gift there in front of the altar. First go and be reconciled to your brother; then come and offer your gift.
NIV