"A culture uniting a nation can either be an historically uniform one, or one that has been forged from the variety of cultures within."

I would say "common" is absolutely fine. It might be a UK/US English difference, I'm not sure. I would also say a common culture can definitely be forged in general terms, but for what you mean, all I can think of are totally different ways of saying it, such as ...uniform or contain local variations. ...uniform or include regional nuances. Something like that.

Grammatically, the sentence is fine. However, so that your readers clearly understand your meaning, you would have to explain in further detail in your later sentences. The word 'unified' is better than the word 'common'. Uniform and forged are sort of odd together. Not incorrect, just requiring more explanation because a culture can be both uniform and still forged.