You can be both.
Not really. You either believe that Jesus is the Son of God, born of the Virgin Mary, was crucified and died on our behalf, rose again, and sends forth the Holy Spirit (also God) to live within us…or you don’t. (This is a simplified version of the Apostle’s Creed, and incomplete.)
Buddhists do not believe in God. They believe in karma. Totally, totally different.
You can’t believe in the Trinity and be a Buddhist at the same time. They are incompatible.
“You can be both.”
Ephesians 4:14
(one version) “Then we will no longer be immature like children. We won’t be tossed and blown about by every wind of new teaching. We will not be influenced when people try to trick us with lies so clever they sound like the truth.”
Also you may want to check out the first of the Ten Commandments. It’s the big one. It says to have no other gods beside HIM. (IE: idols/lucky charms/lean on anything or any person - even the foolish dead people like buddha, Mohamed, etc who swayed millions of people telling them they could find peace (or whatever) inside yourself, in stead of what God says that we humans cannot have peace (or do any good thing) without HIM.
Christians of all flavors don't want to hear that, as you can see. But it is a true statement. I am a Christian but I don't deceive myself into thinking my faith is pure and not poisoned by Western culture and thought. I've found Zen practices to be a good antidote for that poison. Instead of flaming me, just wake me when all the obese, gluttonous believers get rid of their passive entertainment household gods.