Can I drive 3.75 V / 370 ohm coil relay from Raspberry PI GPIO output?
The "3.75V" types are designed for 5V nominal so forget those. They need about 4V to operate reliably and the RPi will give less than 3.3V.  

The 3V nominal types have a 137 ohm coil and will draw about 20-24mA from a 3.3V supply. That's too much to drive safely from the Raspberry Pi GPIO output. You could use a CMOS buffer but it would make a lot more sense to use a small MOSFET or BJT. 

Note: You could parallel two outputs configured to maximum (16mA) drive and it would probably be okay if you can ensure that the outputs are always in exactly the same state. Not a chance I would like to take. The relay would get about 2.8V minimum and they need 2.6 so they'd be okay.