I feel like this is such an interesting question. I've known people who refuse to become involved in organized religion because of the 'rules' and because they don't want anyone 'telling them what to do/believe'. But in a very real way, we're all sort of bound by the religious customs and cultures we've been raised with. Even religious leaders like Jesus, Mani, Zoroaster, etc. who were revolutionary in their particular tradition drew on older teachings and cultural concepts. We do have choice when it comes to our beliefs, but its never a choice made in a vacuum.
I have my doubts on that issue. I think, if you're creative enough and willing to reinvent the wheel from scratch, you can throw off the shackles of your culture. You might have to coin several new words to do it, but I also think that it is within the human capacity. Usually, you can communicate new ideas in old language, though, which I think is quite distinct from being bound to a particular tradition or cultural concepts.
The larger issue is that knowledge is cumulative. Induction itself requires enumerative inference, with science relying on experiment after experiment to take us closer and closer to truth. We are restricted by our culture in this sense. We are also restricted by our own creativity.
When a hypothesis is sustained and all of the alternative hypotheses that interested parties can come up with have either been falsified or shown to be less likely, then that hypothesis is considered corroborated enough to be a theory. The issue here is, what if there is a better alternative hypothesis that nobody has thought of yet? What if there are limitations to human cognition so that we can never formulate, let alone comprehend, the most accurate hypothesis?
I don't think that's a cultural limitation, but a physiological one, and it's one that could possibly be solved. Access to information is a cultural limitation, though, but a lot of that information could potentially be rediscovered.