Such a person is essentially close-minded (everyone is open to ideas similar to their own), and is guilty of what scientists call the confirmation bias.
Merriam-Webster defines close-minded as:
Definition of CLOSED-MINDED
: obstinately resistant to argument or to unfamiliar or unwelcome ideas
According to the Skeptic's Dictionary, confirmation bias is:
"It is the peculiar and perpetual error of the human understanding to be more moved and excited by affirmatives than by negatives." --Francis Bacon
Confirmation bias refers to a type of selective thinking whereby one tends to notice and to look for what confirms one's beliefs, and to ignore, not look for, or undervalue the relevance of what contradicts one's beliefs. For example, if you believe that during a full moon there is an increase in admissions to the emergency room where you work, you will take notice of admissions during a full moon, but be inattentive to the moon when admissions occur during other nights of the month. A tendency to do this over time unjustifiably strengthens your belief in the relationship between the full moon and accidents and other lunar effects.