I read this to say that a theist cannot be open minded, and is prejudiced.
"It depends on what you believe
... and if you already believe, whatever, you're not open-minded; you're prejudiced - which isn't going to help much.
It sounds like perhaps this statement is prejudicial. To suggest that a believer is prejudiced by nature.
Below I replied to JVH's statement:
If an earnest search by an open-minded person results in them becoming a person of faith, in my view they have not lost their "open mind", but their open mind has lead them to a personal truth.
This is certainly how it seems to me. That an earnest and open minded search for truth can result in a logical believe in a God, or a source. That this search resulted in a conclusion does not suddenly "shut" the mind of the seeker. I also believe that it is a philosophically sound conclusion to determine that there is no God. I think both the atheist and the theist have sound logic. We're all wired differently so reach different conclusions on many things.
Anyway, I believe that a theist can be every bit as open (or closed) minded as an atheist.