Is it permissible to send an email to a chip repair company at the father's request, knowing that he refuses to change his musical phone ringtone, and that in this matter he follows opinions that the questioner considers astray and contrary to what scholars have ruled?

There is no sin upon you in obeying your father by contacting the company to repair the phone's SIM card. This obedience is not precluded by the fact that his phone's ringtone is musical, as what is forbidden by Sharia is not the SIM card itself, but rather setting the phone's ringtone to a musical tone. It is recommended for you to gently and wisely advise your father to change the ringtone that is contrary to Sharia.