The driver is isolated, its input is a logic input, with a 200k pulldown:
From your MCU's point of view, it looks like any other logic gate, and current from the 200k pulldown will be tiny, so the MCU's output won't get any significant load.
If your MCU boots up with internal pullups enabled, these will probably be stronger than the 200k pulldown. So if the driver's supply comes up before the MCU has finished booting and initializing the IO pins to output low, you could have a short time when both driver inputs will register a logic high. So it could be a good idea to check what your MCU does at boot, and if necessary add an external pulldown to make sure there is no spurious triggering of the MOSFET during boot.
The inputs have a Schmitt trigger with a good amount hysteresis to protect against noise from switching the power device, so they don't specify any minimum rise time. But if you want to synchronize both drivers, then both signals propagation time and rise/fall times should be matched.
Basically, just connect it to the MCU's output, it will be fine.