Is marrying a girl whose family rejected her due to her affiliation—from the father's side only—with an innovative family, without their consent, considered a violation of Sharia and an act of disobedience to parents, knowing that the girl's and her family's عقيدة (creed) is not innovative?

If the girl is religious and of good character, strive to convince your parents to agree to your marriage to her. Seek help from someone who has influence over them. Their rejection merely because her family adheres to innovations does not obligate you to obey them, nor would you be undutiful by disobeying them in this matter. If there is no harm to you in leaving her, then it is preferable that you seek someone else whom your parents approve of. You must be dutiful to your parents and obey them in what is good. You must cut off all contact with the girl until the marriage contract is concluded.