Which kind of truth?
Organic chemistry doesn't care if you believe in it. Neither does the War of 1812.
Truth is real, it's measurable and it happened. Truth is not in the eye of the beholder.
There are facts that don't change if the observer doesn't believe: The age of the Eiffel Tower. The temperature in Death Valley. The number of people in the elevator.
On the other hand, there are outcomes that vary quite a bit if we believe: The results of the next sales call. Our response to medical treatment. The enjoyment of music...
If you believe that this wine tastes better than that one, it probably will. If you believe you're going to have a great day at work, it will surely help. Placebos work.
We make two mistakes, all the time. First, we believe that some things are facts (as in true), when in fact, belief has a huge effect on what's going to happen. In the contest between nature and nurture, nurture has far more power than we give it credit for. In countless ways, our friends and parents matter more than our genes do.
At the same time, sometimes we get carried away. We work to amplify our beliefs by willfully confusing ourselves about whether the truth is flexible. It makes belief a lot more compelling (but a lot less useful) if we start to confuse it with truth.
But belief is too important and too powerful to be a suspect compatriot of the scientific/historical sort of truth.
We can believe because it gives us joy and strength and the ability to do amazing things. That's enough.