On most Arduino boards, the MPU-6050 will work without level converter.
I like the PCA9306, but I don't like that breakout board by Sparkfun.
The pullup resistors are 1k, which is very low. 10k would be better.
The MPU-6050 is not super strong on the I2C bus, so it might be problem. If you have more pullup resistors it will definitely be a problem.
I use a level converter from Ebay, which works without problem. But it uses mosfets and not a special chip like the PCA9306. So devices on the 3.3V side must also pull down the level on the 5V side.
I read the datasheet of the PCA9306 and I think Sparkfun didn't understand the datasheet about the pullup resistors and what the external devices should be able to do. According to the datasheet: "The external driver must be able to sink the total current from the resistors on both sides of the PCA9306 device at 0.175 V".
So even if you have connected everything okay, the MPU-6050 is not able to pull down the voltage when there is a 1k at the 5V and 3.3V side.