Russia last month invited Saudi Crown Prince Mohammed bin Salman to attend the Oct. 22-24 BRICS summit it is hosting in Kazan. The summit is the bloc’s first since its expansion last year when six new members—Argentina, Egypt, Ethiopia, Iran, Saudi Arabia, and the United Arab Emirates (UAE)—were invited to join.

While countries such as Iran have been quick to accept the invite, the Kingdom has yet to confirm its formal alignment with BRICS. Most likely, Saudi strategists are still weighing all pros and cons of membership...