I recently saw an Instagram post that stated that it's impossible for anyone to be an independent thinker because we're all influenced by our environments and the knowledge we're exposed to. The sentiment was that "no man is an island", and to suggest otherwise is simplistic.
It sounded to me like the author was taking the idea of "independent thinker" or "freethinker" out of context. And by taking it out of context it sounds ridiculous and, therefore, hard to refute.
Of all the people I know who would consider themselves freethinkers, I don't know of any who claim that they are original thinkers, creating ideas independently of others. But, they are aware of their own mental biases, the influence culture has on the way we think, and acknowledge their own ignorance.
And in knowing how their thinking is shaped by both internal and external factors, they choose to side with the truth over their current beliefs. Therefore, being a freethinker isn't about being right or self-reliant, but about acknowledging the influences on our thinking going through a continuous process of revising one's beliefs.
Anyone who considers himself or herself a freethinker and assumes what they know to be true is the ultimate truth, then they have succumbed to the biggest blindspot in critical thinking. We should always maintain a gap between what we think is true and the truth itself. There is always a chance that what we know is false, whether in small part or big.
To arrive at the truth we must be willing to admit what might be uncomfortable for us to admit. Being a freethinker is about having the courage to admit the truth even if it reveals how wrong we were.