Is there evidence that "people in Eastern societies are more in touch with their communities while Western societies value uniqueness more"? In a lecture, a prof claimed that in Western societies, people tend to value independence and uniqueness, whereas Eastern cultures tend to value helping each other and living harmoniously. In a nutshell, people in Eastern cultures think of the community more than themselves, whereas in Western cultures people tend to think about what makes themselves unique.

Are there any studies that relate to these claims?
While I can't, and won't make any comment on the accusations of racism (I think the comments below your question answer that quite well), the Western/Analytic vs. Eastern/Holistic dichotomy is pretty well established and supported by studies in cognitive and social psychological literatures.
This may be a little different to what you had in mind, as your question is more about social notions like 'valuing independence' versus 'coexisting in harmony', which are harder to empirically demonstrate (I'm not a social psychologist).  What I'm referring to here is more like 'logic, rules, and working details out step by step' versus 'taking everything into account, and seeing the bigger picture'.
However, the idea is a bit more complicated than what I'm able to explain in a few sentences.  Nisbett et al's (2001) review (free preprint copy here) is the Rolls-Royce of reviews when it comes to this, and that paper will address most of the questions you might have (note the racial diversity of the authors).
You can also find more work by the same authors here.
References
(just the one)
Nisbett, R. E., Peng, K., Choi, I., &amp; Norenzayan, A. (2001). Culture and systems of thought: holistic versus analytic cognition. Psychological review, 108(2), 291.