All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Allah, The Great and Almighty, has ordered you to be dutiful to your parents and to obey them as long as they do not order you to do something that may be a disobedience to Allah.
The Prophet said: “Obedience is restricted only to what is permissible and reasonable. There should be no obedience to a human being if such obedience constitutes disobedience to Allah.”
Shaving a beard is, without a doubt, disobedience and contradiction to the Prophet's guidance.
Allah Says (what means): {So let those beware who dissent from the Prophet's order, lest fitnah strike them or a painful punishment.} [Quran 24: 63]
'Abdullah Ibn 'Umar narrated that the Prophet said: “Differ from the polytheists: let your beards grow and trim your moustache.” [Al-Bukhari]
Another narration reads: “Differ from the polytheists: trim your moustache and let your beards grow.” [Muslim]
All schools of jurisprudence agree on the ruling of the prohibition of shaving the beard.
Therefore, if your parents' order contradicts Allah's Order, then you have to obey Allah. Also, you have to advise your parents and to guide them to what is good, but in kindness. If they continue to invite you to disobey Allah, it is proved that your advice to them will not be lost and that a patient person will reap good.
In addition, we have issued numerous Fataawa on this subject.
We pray to Allah to guide all Muslims to the right path and to help them to follow Islam.
However, if your parents only order you to cut off what exceeds one's fist from your beard, then you have to obey them since cutting off what exceeds the fist is permissible as proved in the opinions of the Prophet's Companions their followers and the Imams of Muslims .
For more benefit on the limits of obedience to parents, please refer to Fataawa 271255, 131695, and 123554.
Also, for more benefit on keeping the beard, please refer to Fataawa 332320, 317029, 119302, and 91108.
Allah knows best.