IM or BLDC for a go kart?
Is it true?


Absolutely not. The quoted statement is totally nonsense.

However there is definitely a right way and a wrong way to use an induction motor. You must have an inverter that is specifically designed to control an induction motor. More specifically, you need a variable frequency drive (VFD). A VFD will start the motor at a low frequency and proportionally low voltage. To accelerate the motor, the frequency are increased together. If that is done properly, the motor can produce 150% of its rated torque at any speed up to the rated speed.

A sensorless vector VFD can get more out of the motor, more consistently and have an easier set-up procedure. Don't use a VFD designed to drive fans and centrifugal pumps, that is, use a constant-torque rated VFD not a variable-torque model. If a product line lists "standard-duty" and "heavy-duty" models, use the heavy-duty one.

Be aware that you can not get the performance of a Tesla, not even a "scaled down" version of that performance. Both the Tesla motor and the Tesla VFD are very special designs that "are not sold in stores."

Note that a Tesla uses a high battery voltage. You will probably not find an adequate motor and VFD that require a battery voltage less than about 300 volts.

Neither an induction motor nor a BLDC motor are really good choices for the first effort of this sort by someone without experience with those technologies. A DC motor with a commutator will be best in that case.