The Nuance

They are saying that of course they would not mind visiting Buddhist "spots".

Your initial question on the other forum is badly expressed, if I may be forgiven for saying so.

I am unsure if you are saying "As a christian etc. would "you care to" (that is, would you like to) visit Buddhist spots, or if you are asking if their christianity would make them NOT care to visit Buddhist spots. The clarifying sentence "If you’re a Christian in English speaking countries (including, but not limited to, America, Britain, Canada, Australia etc), will you visit Buddhist temples as tourist sites when you take a trip to China or India or Japan?" makes your meaning clearer, though.

Your reply has elicited the question about the meaning of the word "care."

A says:"The spot is dangerous. Don't go there."
B replies:"I don't care."

What B refers to is that he doesn't mind the possible danger in the spot and he will go there.

It shares the same meaning with the word "care" used in my thread.

I don't know why it would cause the uncertainty of your judgment.

You need to phrase questions more specifically - try using more words . eg....

Would you like to visit Buddhist spots ?

Would you visit Buddhist spots that were dangerous ?

care (kâr)
n.
1. A burdened state of mind, as that arising from heavy responsibilities; worry.
2. Mental suffering; grief.
3. An object or source of worry, attention, or solicitude: the many cares of a working parent.
4. Caution in avoiding harm or danger: handled the crystal bowl with care.
5.
a. Close attention; painstaking application: painting the window frames and sashes with care.
b. Upkeep; maintenance: a product for the care of fine floors; hair care products.
6. Watchful oversight; charge or supervision: left the child in the care of a neighbor.
7. Attentive assistance or treatment to those in need: a hospital that provides emergency care.
v. cared, car·ing, cares
v.intr.
1. To be concerned or interested: Once inside, we didn't care whether it rained or not.
2. To provide needed assistance or watchful supervision: cared for the wounded; caring for an aged relative at home.
3. To object or mind: If no one cares, I'll smoke.
4.
a. To have a liking or attachment: didn't care for the movie.
b. To have a wish; be inclined: Would you care for another helping?
v.tr.
1. To wish; desire: Would you care to dance?
2. To be concerned to the degree of: I don't care a bit what critics think.

Thank you.