Just because people don't talk doesn't mean they don't think.
Some people(non-native speakers) say this is grammatically incorrect. It is acceptable in casual conversation, but it should not be used in business or formal speech. They say, grammatically speaking, "Just because people don't talk" cannot be the subject of the sentence.
Is this true? I often use this type of sentences.
It's perfectly grammatical. It's mainly an informal sentence pattern, and so it's true that it's usually avoided in formal style—but that's not because it's ungrammatical. Grammaticality and formality are two very different things.
The basic pattern looks like this:
(just) because + clause + does not mean + that-clause
This is covered in The Cambridge Grammar of the English Language (CGEL) on page 731:
Because is the most central and versatile of the reason prepositions. A PP with because as head can occur in subject or predicative complement function as well as adjunct:
[24] [i] Because some body parts have already been turned into commodities does not mean that an increasing trade in kidneys is desirable.
[24] [ii] The reason I didn't call you was because the phone was out of order.
Because could be replaced by the fact that in [i], that in [ii], and these latter versions would be widely preferred in formal style. In the subject structure [i], because is often modified by just, and the matrix VP is more or less restricted to doesn't mean: Just because you're older than me doesn't mean you can order me around.
As you can see, this sort of PP can occur in subject position, although it's basically limited to this particular sentence pattern (as CGEL says, "the matrix VP is more or less restricted to doesn't mean").
One last note: grammar is a description of how native speakers use the language. Certain learners may be unwilling to recognize because-PPs in subject position, but if native speakers regularly use and accept them anyway, all this means is that the grammatical description used by those learners is inadequate.
It depends who you ask.
To many folks who answered the ELU question Sentence Construction: “Just Because … Does Not Mean”, it seems it is ungrammatical.
However see also this response to the contrary under Can a “because clause” be a subject clause? [duplicate]. See also the answer by snailboat that cites the CGEL.
According to explanations found in many traditional grammars, the because clause forms a subordinate clause and cannot be used as a subject. According to this line of thinking, this is just as ungrammatical as the sentence without just:
Because people don't talk doesn't mean they don't think.
Frankly, the version without just sounds "off" (questionable) to me. For those who find this ungrammatical, they might point out that using a different conjunction is just as ungrammatical:
Whenever people don't talk doesn't mean they don't think.
Therefore, some would say that the grammatical version is:
Just because people don't talk, it (or: this/that) doesn't mean they don't think.
However, as noted, the original version is certainly used in vernacular or everyday speech.
Now we come to the power of the people. If the people want to use "because" in the same way they use that, then the sentence can be judged as grammatical--although this may not be accepted by everybody.
As for the that clause, it is grammatical to say/write:
That people don't talk doesn't mean they don't think.
This is grammatical, (subordinate 'that' clauses can function as the subject) but people don't go around talking like this. Perhaps this is one reason that the specific construction you ask about is popular.
However, you may find it practical to appease everybody by not using the (just) because versions in writing and formal/business speech.
I think your sentence is the way people talk. But if you want better grammar I suggest
