"Ich bin eher offen."
I don't think so. 'fairly' or 'pretty (much)' would match 'ziemlich' here. 'eher' is low-key, contained in this sort of context, when someone isn't very sure of or commited to something.
How are you acting towards unknown persons? - I tend to be rather (eher) vs. pretty (ziemlich) open-minded towards them. I don't think they're interchangable, since they depict different shades of the corresponding word.
Thanks for clarifying that. I was surprised "ziemlich" wasn't accepted. I always considered "rather, quite" to be of the same shade as "pretty much, fairly" though so I guess it's a matter of semantics here.