XLRI doesn't have any kind of religion-based cut-off nor any reservation on caste-based. As XLRI is one of the most reputed colleges in India, the percentile required for non-christian is the same as for a Christian candidate.

Cut-off depends totally on the performance you have done in your exam. Above 90% is required to appear in GD and PI and after that, you get your seat. No institute has based cut-off based on religion, castes in the world.

In the Indian education system, no one can bias on the behalf of any caste, religion, sex, it all depends on your performance and your outcome will tell your future. Don't think about anything just focus on your studies make a strategy and implement it if you want to crack your exam.

Using words like "tyrannical" and "miserable" seems harsh. Your information source might have exaggerated the situation at XL. Compared to other B-schools, the students at XL enjoy similar, if not more, freedom. A student body has a say in negotiating with the administration, and they have been able to change administrative decisions in the past. The administration does play a role in maintaining discipline on campus, but students also have a responsibility to represent the school well. Overall, students at XL have a memorable experience, and administration interference in day-to-day life is minimal.

My elder brother used to be a student of XLRI and he had to come across some tricky, if not weird questions. 

• They asked him the difference between a lion and a tiger, the difference between a penguin and a bird. They asked him to differentiate between an alligator and a crocodile, between a turtle and a tortoise, and also between a donkey and a mule.
• He had to refer to the group discussion where the professor asked my brother to rate the group and how he contributed. 
• The professor asked him about the error of commission and the error of omission. 
• He could not say if the professor was satisfied with his answer and all he got in response from the latter was a straight face.
• Other questions the professors have asked their interviewees were the difference between the tragedies of Sophocles and Shakespeare. It is a good question to test our knowledge of dramatic narratives. 
• Another question was how Shakespeare can be related to human resources.

Interviews in B-schools can sometimes be non-standardized and are often reactive of the experiences of the interviewee(s). My brother cannot say if the testing is deliberately non-standardized, whether responses are calibrated or normalized, or if the professors test the reliability. A lot of people who made it past the personal interview ended up joining the IIMs and vice-versa.

The answer is yes, students from lesser-known colleges do make it to XLRI. Getting admission into XLRI depends on several factors. If you fit their profile then surely you will get accepted. The basic requirements include the following -

The weightage of these factors varies every year. The marks obtained in the graduation helps in giving an edge during group discussions and personal interviews. Once a student clears all the factors and gets into the interview session, everything else is secondary. It all then depends on how well you perform and impress the interviewers. But if you are from a lesser-known or smaller college and are well prepared, then they will definitely consider you.

Students from various nooks and corners of the country get into XLRI. You should stop worrying about their college and focus more on their entrance exam, GD and PI.