The OP asked 3 questions:
- But if the forward voltage of blue diode is said to be same as supply voltage of my GPIO pins, how would then things work?
What this means is that the manufacturer has integrated a resistor with the LED. This relieves you of having to size the resistor yourself, and insert another component in your circuit. The manufacturer has chosen the proper resistor value for connecting the LED across a 3.3v supply (RPi GPIO pin for example).
- Will the rpi be just 'unable' to power up the led? And if it will (and diode will do just fine with lower voltage),
The RPi will be able to power up the LED from any 3.3v output. If you reduce the voltage below 3.3v, the LED will still light up when this lower voltage is applied to a point. At some point, if the voltage is low enough, the LED will no longer illuminate because the forward current is too low, or your supply has not forward-biased the LED.
- how should I calculate resistor value?
Again, as long as the LED has an integrated resistor (which will be the case when the LED is specified as a "3.3v LED"), then you need not calculate, or add, another resistor to your circuit.
Finally, you should always consult the spec sheet published by the manufacturer for the device as the "ultimate authority" in these matters. Spec sheets are available online from a variety of sources. Mouser's website is one I use; they list a large number of 3.3v LEDs in their catalog.