It heavily depends on your definitions of both those terms. However, strictly speaking, patriarchy in itself while still constraining of women (an egalitarian society would be much better), also required heavily duty-bound behavior from men. Something which is not conducive to open or effective misogyny.
I do not know of any societies with strong patriarchal norms and very little misogyny, if they do indeed exist.
Patriarchy in cultures is without fail about the control of women. All niceties around protecting them boil down to treating them as property, as chattel. You fundamentally don't have an equal situation when one gender is rendered property of another.
I do not know of any societies with strong patriarchal norms and very little misogyny, if they do indeed exist.