Open-mindedly

adv.thoughtful, kindprofessional

What it means

With fair consideration for unfamiliar ideas or views.

Reach for it when describing fair consideration of an unfamiliar idea before judgment

Jon listened open-mindedly when residents proposed a different route.

everyday
fairly
each view receives just consideration
not when Fairly can also mean to a moderate degree.
everyday
with an open mind
the familiar phrase sounds more natural
not when The expanded form states an intention, not a result.
warm
curiously
genuine questions guide the response
not when Curiosity can coexist with a fixed conclusion.
professional
impartially
competing views are treated evenly
not when Impartiality can create false equivalence.
professional
receptively
new information is welcomed
not when Reception does not require critical evaluation.
formal
without prejudice
prejudgment should be explicitly excluded
not when The phrase can carry a legal tone.

listen open-mindedly
Jon chose to listen open-mindedly to the residents' route proposal.
consider open-mindedly
The panel will consider open-mindedly any supported alternative.
respond open-mindedly
She responded open-mindedly while still asking for evidence.

Open-mindedly is grammatical but uncommon; 'with an open mind' is usually more idiomatic.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.