Where is the line between open-minded and wishy-washy?

I like Fluther (although I often have to limit visiting because I have things I have to do that don’t involve hours upon hours of Fluthering) in part because I find my views being challenged on a regular basis, by generally intelligent, logical, civil people who often have very different views than mine.

I have been in lots of debates about lots of topics, and I have really, really strong opinions. But I find myself questioning my ideas a lot when I am on Fluther. I think challenging one’s opinions is a great thing, and something everyone should seek to do on a regular basis. But it is uncomfortable, and I think that is why people avoid it.

My question is where is the line between having a truly open mind, where you are not afraid to have it changed, and being staunchly opposed to any change in perspective? There are those who will support any viewpoint from any slick-tongued sophist, and those whose beliefs are so ingrained that they can’t (or will never) see reason.

Where is the line?