Like a pot calling another pot black. While Saudi Arabia does have an inconvenient human rights record, so does India. India have already become a theocratic state, just like Saudi Arabia, only with a different religion. Both countries pushed forward policies that favour their their preferred religion. Both countries are not too fond of their religious minorities.
Problem for India is, the other BRICS member want Saudi Arabia onboard. Not because they adore Saudi Arabia. But because pulling SA over would be a big win in the great game against the West. India have been stonewalling the BRICS for awhile, but somehow also expects to have a big say in things. This is the Indian mindset. They don't have the concept of earning their power and influence. They just feel that they are entitled to push people around.
There is a view going around that India would one day quit the BRICS and SCO due to irreconcilable differences with it's other members. But my understanding of the Indian mindset is that India will never quit. Instead, India actually wants to hijack both organisations to its own benefit. India's ultimate goal is to become the leader of both the BRICS and SCO, to kick China and Pakistan out, and to invite more of its own minions in. So India will not quit on its own volition. It needs to be forcefully ejected. This is a very uncomfortable thing for BRICS and SCO to do, because both wanted to present themselves as open-door, and inviting organisations. Both organisations are also in recruitment mode, so they don't want to create a negative image by kicking out a major member. Also Russia, being very fond of India, might still want to very much keep India in SCO and BRICS. Nevertheless, India is still a cancer in both organisations. The longer it stays, the stronger it's influence grows, the more 'sick' both organisations become.
So, I think the most realistic way forward for SCO and BRICS is a managed isolation of India. India could be given lip-service, but at the same time, given the cold shoulder on important matters. Either India eventually throws tantrums and quit, or just stays comfortable in cold storage. Still, I predict that the biggest challenge to carrying this out is getting Russia onboard. Russia will have to man up and make that difficult decision. Russia either has to choose to pursue its own proclaimed destiny of being a pole in the new multipolar world, or being held back by a self-interested India.