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.