But we do. What about the following sentences (from COCA)? Are they not about qualities or states?I have no problem with the meaning of open-mindedness, only its use with keep - to me that is totally unidiomatic, we just don't use keep with states or qualities.
I would also make this distinction.But "kept an open-mindedness" and "kept an open mind" have different meanings. Keeping an open-mindedness refers to a general attitude to all events and experiences. Keeping an open mind usually refers to an attitude to particular circumstances. Thus, somebody who keeps an open-mindedness is likely to have an open mind every time that they come across new experiences or questions. It is not surprising that open-mindedness has far fewer hits in an on-line search.
So your objection to it is a matter of style, not of grammar or meaning. As e2efour commented in post #2.As I said, my main objection is that it doesn't sound idiomatic or natural to me ... but I do find the simple version with 'keep' just too like the existing idiom for comfort.