I want to increase my gear range, will my front gears affect the cassette I can use? I'm contemplating increasing my road bikes gear range. I have a race coming up that has some significant climbing. My question is if I want to increase the teeth on my rear cassette will that be limited by the type of gears I have at the front? My set up currently is a Shimano Claris FD 2403 front mech, Shimano HG50-8 11-30t cassette. Would I be able to increase the cassette to 32t or more without it being incompatible with the front mech?
Your cassette won't affect your front mech. You may need a longer chain, and your rear derailleur might not be designed to handle the larger cassette, but that's another question.

Also, the difference between a 30-tooth and 32-tooth gear is barely noticeable. Go for a 34-tooth low gear.