The answer is “not discriminating.”
Here is an excerpt from the poem to explain how I arrived at that answer.
“She had
A heart—how shall I say?— too soon made glad,
Too easily impressed; she liked whate’er
She looked on, and her looks went everywhere.”
This excerpt is basically saying that the Duchess would look at everyone with happiness, and was very easy to please. This means that she did not discriminate against certain people. She “liked whatever she looked on.”