Is it permissible for a Muslim person to always use they/them pronouns for themselves instead of she/her or he/him?
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.
In principle, it is permissible to speak about oneself in the plural pronoun, such as a person saying about himself “we” or “our” or talk about a singular person by saying: “they” or “them”.
Ali said: “The Messenger of Allah put me in charge of slaughtering his camels (which he wanted to sacrifice); and to give in charity their meat, skins, and saddle cloths; and not to give any of them to the butcher. He said: We give him from ours.” [Muslim]
The evidence from the Hadith is his saying: “We give him from ours”; while it is known that the Prophet was very humble.
Allah knows best.