How can a father be persuaded to agree to his daughter's marriage to a young man whom he rejects for reasons related to his place of birth, work, military service, and some rumors about his father, while upholding filial piety?

The guardian is not entitled to reject a suitor who is suitable; this is considered 'adhl (unjust prevention). The girl's father should not pay attention to people's talk about the suitor's family unless there is clear evidence. The suitor might be a person of religion and good character, and thus should not be held accountable for his father's sins.