Is this sentence correct?
"For me, in fact, it is really important to knowing people that may make you culturally richer"
Should it be "important to know" or "important to knowing"?
What's the difference and why?
The sentence, as constructed, is not correct. "is important" would be followed by the infinite form of a verb. I can't find a definite reference on the Internet, but Cambridge Dictionary has several examples of "is important to [infinitive verb]" format.
If you wanted to use gerund, you would typically use the form "[noun phrase] is important". So, your options are as follows:
For me, in fact, it is really important to know people that may make you culturally richer.
For me, in fact, knowing people that may make you culturally richer is really important.
For me, in fact, to know people that may make you culturally richer is really important.
These are all sentences where we only refer to one thing (to know people) and say that it's important, i.e., "X (gerund/infinitive) is important" or "It is important to X (infinitive)". We are not specifying what X is important for.
On the other hand, if we look at the the sentence from the OP's forum link, it is of the form, "X is important to Y". In this case, you can use gerunds or noun phrases to describe both X and Y. For example:
(Gerund) Good humidity, even moisture, and bright light are important to growing this species well.
(Other noun phrase) Good humidity, even moisture, and bright light are important to the growth of this species.
(Gerund for both X and Y) Having access to a lot of books is important to being a well-read person.
Contrast this with "It is important to X (infinitive)" form:
It is important to have good humidity and moisture. (No information on what those are important to.)