The "People Will Believe What They Want" objection

This is a follow-up to my Open-Mindedness Post

Theists often levy the following objection to arguing religion, "No matter what you say, people are going to believe what they want to believe. Regardless of science, evidence, or anything else, people aren't going to change their minds." Some extend this to "Whatever you say, I won't change my mind" or "I don't care what science says, I'm not going to change my mind." What, other than this, could more accurately demonstrate closed-mindedness?

"No matter what you say, I won't change my mind" is a horrible position to take. If extraordinary evidence is presented to challenge your position, you should consider it, start independent research via reading books and listening to debates, perform a thorough investigation, really think about the issues, and make a choice based on good reason. If, for example, very good arguments for God's existence were presented or God revealed himself to everyone in an indisputable fashion, I'd change my mind...or at least really consider the objections.

Would you accept this argument or levy it in non-religious situations?
"I will believe that [the earth is flat, drinking Lysol is good for my health, Germany is located in Canada, the planet Saturn doesn't exist] no matter what you say! No, this position is untenable. Pro-life individuals have told me on numerous occasions that "I believe a life is a life from conception no matter what science says!" This position is not only intellectually dishonest, but simply false. Cells that are not fully human beings are not human life. Potential life is not life. Etc, etc, etc.

If science shows that life is not life until the third trimester and backs this statement with good and hard evidence, we should accept the idea. If science shows that the earth is older than 6000 years old and backs this with hard evidence, we should also accept this idea.

Consider objections.
Think about your beliefs.
Be willing to change your mind if the evidence is presented.
Don't be closed to ideas simply because you disagree with them.