One MOSFET slowly activates itself, the other won't fully activate
The voltage drop across the resistors in series to the green and blue LED might be part of the problem.
If each LED really needs 700 mA, the voltage drop across the resistor for the blue LED would be 1.4V. This would leave 3.6V for the blue LED forward voltage and the Vds of the MOSFET. This might just be enough but I wouldn't bet on it.
For green, the voltage drop across the resistor would be about 2.5V, leaving only 2.5V for the LED and MOSFET's Vds. This probably isn't enough.
And as @Transitor recommended, I also wouldn't use the 100 Ohm from Gate green to GND. Besides the potential divider this will draw quite a lot of current from your GPIO. You should alos check if your 5V supply can source the 2.1A for all three LEDs.
Some ideas to solve the LED issue:

Make resistor green and blue smaller. Probably the easiest solution but with ill defined LED currents.
Use a BJT with a resistor in the emitter as a constant current source providing 700mA. This however might need more than a 5V supply.