Can someone be inadvertently sexist

Yes, you can be inadverdantly be sexist by example of your elders or by misplaced instinct .

If someone accuses you of sexist behavior, you best bet to avoid a confrontation is to say : Excuse me, I am not very familiar with this subject, but would appreciate some advice if you care to give it. " This wil render you a non-threat and possibly make you a new friend, by showing your willingness to learn new attitudes.