The first is a set up clause. The second contradicts it.

There's am implied "but" after the comma (although it doesn't fit for this particular sentence structure, the idea remains)

For example, "For a lot of healthly athletes, a burger from McDonalds is still a nice treat."

You wouldn't say this statement claims McDonalds is a healthy place to eat. It is saying these people are healthy, BUT they still do things that are unhealthy.

For Clinton's statement: These people are otherwise well meaning and open minded, BUT they are still fearful.."

Combine this with her following sentence which you clip cuts out, then you have a statement that only a crazy person could find fault with.