Praise be to Allah.
The basic principle is that the parents have no right to object to their child following the Sunnah and noble Prophetic teachings, whether those Sunnahs have to do with the rights of Allah and acts of worship, or interactions with other people, morals and manners. The Islamic texts which enjoin obedience to parents are based on the requirement to treat them kindly, take care of them, look after their affairs and avoid upsetting them, even by one’s words. There is nothing in those texts to suggest that the son should obey their instructions outside of this framework. There is nothing in them either to suggest that obedience to them should be given precedence over obedience to Allah and His Messenger.
Imam as-Sarkhasi (may Allah have mercy on him) said:
With regard to any journey that a man wishes to undertake, apart from jihad, whether it is for the purpose of trade or Hajj or ‘Umrah, if his parents object to that, and he does not fear that they may be neglected and face hardship in is absence, then there is nothing wrong with him travelling, because in most cases such journeys are safe, and they will not experience severe hardship as a result of his departure. Grief at his absence is warded off by the hope of his safe return. But if there is any fear of danger to him in that journey, such as if he is travelling by sea, then in that case the ruling is the same as the ruling on his going out for jihad, because the danger of death in that case is more obvious.
With regard to travelling for the purpose of acquiring knowledge, if the route is safe, and it seems that the place to which he is headed is safe, then it is no different to travelling for the purpose of trade. In fact this is more important, because Allah, may He be exalted, says (interpretation of the meaning):
“out of each community, a group should go out to gain understanding of the religion”
So there is nothing wrong with him going out for that purpose, even if his parents object, so long as there is no fear of them being neglected and facing hardship in his absence.
End quote from Sharh as-Siyar al-Kabeer (196-197)
Shaykh Abu Bakr at-Tartooshi said in his book Birr al-Waalidayn:
There is no obedience to parents with regard to giving up a regular Sunnah, such as attending prayers in congregation, or not praying the two rak‘ahs before Fajr, or Witr prayer, and so on, if they ask him to give that up on a permanent basis.
This is unlike the case if they call him when the time for the prayer begins; in that case it is obligatory to obey them, even if he misses out on the virtue of praying when the time for the prayer first begins.
End quote from al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (8/71)
We have previously quoted a statement of the fuqaha’ concerning this matter, and have explained the guidelines on obligatory obedience to parents in some detail. That is in fatwas no. 1176, 1185, 40283, 98382, 101105, 166428 and 174831
However, the child should excuse himself to his parents by speaking kindly and in a good manner, discussing the matter politely, so as to avoid worse problems – Allah forbid. In all of that, he should affirm to his parents the virtue of the Prophet’s Sunnah and the etiquette prescribed in Islam, and he should make up for not obeying them in that matter by serving them in other ways, giving them a gift, or compromising in some other matter, so that he may reassure them.
Regardless of whether shaving off the beard is haraam or makrooh, neither the parents nor anybody else has the right to issue instructions that are contrary to the command of Allah and His Messenger. The Messenger of Allah (blessings and peace of Allah be upon him) instructed that the beard should be allowed to grow in more than one hadith.
An exception to that is if letting the beard grow in some country maybe a direct cause of exposing one to persecution and danger. In that case we would advise him to listen to his parents’ request out of mercy and compassion towards them, so that no hardship will befall him that would cause them distress.
And Allah knows best.