One Source: 4

We can now understand the idea that Rabban Gamliel shut the doors of the Yeshiva to anyone who was not the same internally as externally. He was turning away students who appeared superficially (and perhaps even in their own minds) to be seeking personal growth, but had not yet determined that the Yeshiva was the place to which they would permanently attach themselves to find that growth. The student appeared to be "getting with the program" but internally he wasn't really there.
The success of the studies is predicated on the teacher-student relationship and requires a completely trusting relationship between them. One student who is not willing to commit himself to that extent, can harm the experience for all of them.

One Source: 1

Our Sages tell us that at one point Rabban Gamliel instituted a rule that only students who were the same internally and externally (תוכו כברו) were permitted to enter the Yeshiva.
Why was this rule instituted?
There are times when a person can study under one teacher for many years and enjoy his studies as the teachings are wondrous, however, internally he remains the same person. This results from the fact that he is not entering into his studies in a manner analogous to marriage. In other words, he is not truly connecting to the inner meaning of his teacher's words. All his studies are superficial. All the spiritual talk and discussion is very enjoyable, but he doesn't absorb them into the essence of his being.
He may even find after time that behaviorally he has changed to some extent, but his internal world is no different than it was the first day he began his studies. With all the wonderful discussion, nothing has entered his soul.
He is like a merchant who travels from fair to fair, cutting deals, buying and selling, but at the end of the day he hasn't turned a profit to bring home.