Word that means "more accepting of other cultures"?

tolerant would fit.

1

willing to accept feelings, habits, or beliefs that are different from your own

2

An individual can be tolerant, and so can a community or a nation if it accepts people from lots of different cultures or backgrounds

Cosmopolitan may suit your needs depending on the connotations you're after. It suggests an awareness of global culture and is also an antonym of provincial (in the “small minded” sense).

multicultural is the current mainstream intellectual word for this.

I've heard the word 'inclusive' used to describe this kind of behavior in the corporate setting.

I would say that the person would be open-minded or an internationalist.