Is it essential to move one’s ring when doing wudoo’ and ghusl?

If the ring is loose enough for water to get underneath it,
then it is not necessary to move it. But if it is so tight that water cannot
get underneath it except by moving it, then it has to be moved. That applies
in both wudoo’ and ghusl. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (11/30): 

The majority of fuqaha’ are of the view that it is
obligatory, when doing wudoo’, to move one’s ring when washing the hand, if
it is tight and he does not know whether the water is reaching the skin
underneath it. But if the ring is loose, or if it is tight but he knows that
the water can reach underneath it, then he does not have to move it; rather
it is mustahabb. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was
asked: Is it essential to move one’s ring and watch when doing wudoo’? He
replied: The fuqaha’ said that it is Sunnah to move them. 

But if it is tight, it is essential to move it, because if it
is not moved the water will not reach what is underneath it and Allah, may
He be glorified and exalted, says (interpretation of the meaning): “…wash
your faces and your hands (forearms) up to the elbows …” [al-Maa’idah 5:6].
So it is essential to wash the entire hand, from the fingertips to the
elbow.

End quote from Liqa’ al-Baab al-Maftooh, no. 232 

And Allah knows best.