If you have a BMS, will current be limited at some points to a DC motor and affect performance?
BMS cutouts - high voltage, low voltage &amp; over-current are intended for "when things go wrong" - not as primary control systems. BMS balancing is a proper function of the BMS in normal use, but in normal operation only occurs when the battery is very close to fully charged. 

You, and/or your professor, are confusing different actions of a BMS.

Cell balancing occurs during charging and with the balancer you refer to they say


  "When any one cell in the battery pack exceeds the Start Balancing voltage, the BMS will begin the balancing algorithm for all cells." 


About the only situation that would occur in is where the batteries were fully charged and you had regenerative braking and immediately commenced a downhill braking procedure.   

Regardless of whether you were able to trigger this mode in some manner, it is not associated with high current motor operation. 

The professor may have intended to refer to or referred to over current battery protection.  Under conditions of very high discharge with two parallel batteries, each with its own BMS, it is essentially certain that one BMS will reach trip point before the other. How soon depends on both BMS trip point settings and the degree to which the two batteries share the load current. 

For purposes of example assume your cells are high power 18650s rated at 30A max discharge and that you set the BMS at 40A trip. That's per 5S battery so the total allowed output is 60A x 5S or about 3.6V x 80A  ~= 300 Watts typically. 

At 40A/battery wiring resistances of 0.01 Ohms will drop 0.4V.
That's liable to be well in excess of BMS settings imbalances.
Even a wiring resistance of 0.001 Ohm drops 40 mV.
So you need to aim at differences in wiring loom resistances for the two batteries of around 1 milliOhm or less.

If cell internal resistances vary by more than a few milliOhms you'll get similar effects ven with perfectly balanced wiring.  

What this seems to be suggesting is that if you really MUST push your bike to it's max power limit without tripping one BMS - and so then the other, that you functionally need a single BMS - perhaps independent strings of electronics communicating intelligently.

But, odds are, when you are that close to the limit the sequential tripping is just a sign that the system has reached its limit and is about to trip out, no matter what you do.

A logical "solution" is to set your main controller so that it never allows current to reach the BM trip point.  

Again: BMS cutouts - high voltage, low voltage &amp; over-current are intended for "when things go wrong" - not as primary control systems.