From my knowledge, it night be quite difficult to practice both, but still might be possible. The Buddha had a few quotes that contradict the teachings of Jesus.
The Buddha said:
‘There are some monks and priests who believe that whatever pleasant, painful or neutral experience someone has, all that is due to a supreme god. I approached them and asked if they believed this and they said they did. Then I said, “So according to you, if someone is a murderer, thief, adulterer or liar, a foul-mouth, greedy, hate-filled heretic, all that must be due to a supreme god.” When someone falls back on a supreme god as the answer, there (should logically be) no will to do, no desire to do, no necessity to do this or avoid that. Such a person is confused, vulnerable and cannot honestly call themselves a true monk or priest. This is my rightful refutation to those who believe such ideas, such views.’ -The Buddha (Tittha Sutta)
The other one I know about is the following:
‘Why does God not straighten out the world? If he really is the Controller, the Highest, Lord of All Beings, why is the whole world in such a mess? Why did he not make the world happy? If he really is the Controller, the Highest, Lord of All Beings, why is there so much deceit, lies, pride and unrighteousness? If he really is the Controller, the Highest, Lord of All Beings, then he must be unrighteous and cruel because it was he who made everything.’ -The Buddha (Ja. VI,208
In the Kalama Sutta, the Buddha makes it clear of when a teaching should be accepted:
"Do not believe in anything simply because you have heard it. Do not believe in anything simply because it is spoken and rumoured by many. Do not believe in anything just because it is found in your religious books. Do not believe in anything merely on the authority of your teachers and elders. Do not believe in traditions because they have been passed down for many generations. But after observation and analysis. When you find that anything agrees with reason and is conductive to the good and benefit of one and all, then accept it and live up to it." -The Buddha (Kalama Sutta)
Here the Buddha makes it clear that you must not believe in anything on faith, and Christianity takes a little faith, no? I am also sure that there are Bible verses, and denominations of Christianity that might not allow you to follow Christianity with other religions.
Now don't get me wrong. One could still follow the Eightfold Path that was taught by the Buddha while believing in Jesus Christ.
- Right view
- Right intention
- Right action
- Right speech
- Right livelihood
- Right effort
- Right mindfulness
- Right concentration