Depends what your definition of open-minded is?
Having a strong faith in a particular belief is the sign of someone with conviction in their choices.
For me being wishy-washy and spending your life fence-sitting is just a lack of conviction that is not open-minded.
Open-minded is allowing for new experiences and making decisions on them. Just accepting all directions as options without any kind of opinion is not really experiencing them.
I look deeply at all options available to me and made an informed choice based on knowledge and experience to become a Jehovah's witness. I have commited to that choice now but I can speak knowledgeably about the ones I rejected.
If someone chooses to be an Atheist the same way I respect that.
I am sure that they would agree with me that we make choices and accept the consequences of those choices which is the essence of freewill. We can't then conplain if we are wrong.
So making choices that lead to conviction of opinion is not a sign of lacking openmindness IMO.