Is it permissible for a girl to marry without her father's consent if he refuses to marry her to a religious young man, despite her religiosity and her having committed adultery with the young man?

You must sincerely repent, regret the sin, and cut off the relationship with that man, for Allah has commanded sincere repentance for sinners. Your actions make your marriage forbidden until you both repent, along with the completion of the fornicatress's 'iddah (definition) (waiting period) and her repentance. If these two conditions are met, then her marriage becomes permissible.

As for the guardians, they must fear Allah concerning those under their guardianship and marry them to those whose religiosity and character they approve, otherwise, great discord and corruption will ensue. There is no excuse for a girl to fall into fornication, nor to marry without a guardian, for her marriage contract is invalid. Guardians should not refuse someone who is religiously suitable. If a guardian prevents a woman from marrying, she has the right to refer her case to the judge to transfer the guardianship.