What are the rules and yardstick for one to become an upanyasakar? Forgive for asking this – over the last few years, Christians, non-brahmins, women have become upanyasakars and preach the meaning of Rahasyam. It his right?

To become an upanyasakar to preach Bhagavad Vishayam, primary requirement is that one must learn and well understand Bhagavad Vishayam through a qualified preceptor. Only after this and only when permitted by that preceptor can one preach to others. Without the Acharya’s permission, this must not be done.
It is not appropriate for those who do not belong to the tradition to talk about the messages of tradition. What they say might be different. No need for Srivaishnava-s to listen to such talks. If the upanyasakar has learnt it from a preceptor and preaches with the permission of the preceptor, we can list to them, even if they are women or non-brahmins.