If I encounter anything that contradicts the Word of God, you can expect me to do exactly what Jesus does when He encounters words that contradict His Word:
"While He was still speaking, there came some from the ruler’s house, who said to Jairus, Your daughter has died. Why bother and distress the Teacher any further?
Overhearing but ignoring what they said, Jesus said to the ruler of the synagogue, Do not be seized with alarm and struck with fear; only keep on believing"
~ Mark 5 v 35-36
He's our Rock, and His Word is final. Don't let words of unbelief enter your heart. Just as Jesus did, if you hear them, don't take them in. Jesus gives you permission to ignore unbelief - not being rude, but simply not taking it on board - and focus on His Words, for He has the words of eternal life (John 6 v 68).
In the above example in Mark, Jesus ignored the reports, and urged Jairus, the girl's father, to just believe. Believe on what? On Him. Jairus had come to Jesus with faith that He could heal his daughter. Jesus didn't want a worsening report to affect that faith he had. Jesus went on to raise the girl up from death. The more we use our faith, the stronger it will get, and won't be swayed as easily with the storms of life.
Jesus' word is final. Make sure the words of others do not cause your faith to waver.