Did Ramakrishna Math and Mission dissociate from Hinduism?
Ramakrishna Math and Mission never dissociated from Hinduism. What happened during that time is associated with the politics of that time. The Jyoti Basu run Communist government at that time was trying to infiltrate and take over every private organization in West Bengal. Ramakrishna Mission schools and colleges were also targeted by the Communists. You should remember that the Communists considered Ramakrishna as an illiterate epileptic and Vivekananda as a Hindu fanatic. Ramakrishna Math was afraid that the Communists would take over their schools and indoctrinate the students with Marxism and teach them to hate Ramakrishna and his teachings. So they contacted lawyers to take the left government to court. The lawyers told them that the only way to save the organization from Communist takeover was to declare them a non-Hindu organization since only non-Hindu organizations are protected from political interference. The whole thing was a legal maneuver to gain time. The maneuver stalled the Communists for 20 years and by the time Ramkrishna Mission lost the case the Communists were too weak to take over the Ramkrishna Mission organization.
Some people accuse the Ramkrishna Mission of cowardice. All I can say is that they have not lived through the left terror inflicted on West Bengal during that period.
Does the Ramkrishna Mission teach that all religions are same?
I would say no. They do teach that all religions are paths to truth but not the same. I have given below Swami Vivekananda's explanation of their position.
You must remember that humanity travels not from error to truth, but
from truth to truth; it may be, if you like it better, from lower
truth to higher truth, but never from error to truth. Suppose you
start from here and travel towards the sun in a straight line. From
here the sun looks only small in size. Suppose you go forwards a
million miles, the sun will be much bigger. At every stage the sun
will become bigger and bigger. Suppose twenty thousand photographs had
been taken of the same sun, from different standpoints; these twenty
thousand photographs will certainly differ from one another. But can
you deny that each is a photograph of the same sun? So all forms of
religion, high or low, are just different stages towards that eternal
state of light, which is God Himself. Some embody a lower view, some a
higher, and that is all the difference.
The Complete Works of Swami Vivekananda, IV, Christ the Messenger
It would be impossible for Ramkrishna Mission to say that all religions are equal. Can they agree with the alleged statement of Jesus, 'I am the way, the truth and no one can come to the father except through me' (my paraphrase)? Obviously not. Vivekananda says quite clearly that Vedanta embodies the highest view and other religions lower view. All religions are not the same.