Arduino Pro Micro and multiple MPU6050s

What makes you think you need shift registers.

Generally speaking,
the address pin (if available) of I2C devices can be used as "chip select" pin.
Join all SCL, SDA, VCC, GND pins, and connect the address pin of each device to a digital output pin.
Make one HIGH (or LOW) at the time, and ten talk to that unique/selected I2c address.
Leo..