Both of them asked me to be a free tour guide during their stay in Shanghai, while Ieven though I had never chatted with any of the people who sent messages.either of them.

I can't understand {the construction of this kind of brain | how their minds work | how they think}.

Maybe social distancing(?) has different meanings in different countries?

I agree with the other corrector — “personal space” might work better than social distancing here. Social distancing is an infection control technique:
https://en.wikipedia.org/wiki/Social_distancing

Both of them asked me to be a free tour guide during their stay in Shanghai, while Iereas I have never chatted with any of the people who sent messages.

I cadon't understand the construction of this kind of brain.how they think.

Both of them asked me to be a free tour guide during their stay in Shanghai, whileeven though I never chatted with any of the people who sent those messages.

1. I think that "while" doesn't really capture the sense of contrast that's implied here. "Even though" or "despite the fact that" are more suitable.
2. A more natural way to end the sentence would probably be "even though I never chatted with either of them", since you've already mentioned the two people earlier in the sentence.

I can't understand the construction of this kind of brain.

This is a perfectly fine sentence, but I think the phrase I hear most often in this kind of situation is "I don't understand how some people's minds work".

Maybe social distancing has different meanings in different countries?

"Social distancing" usually refers to an immediate kind of distancing, like the 2 metre rule during the pandemic. If that's what you meant then this sentence is fine as is.
If you meant something more along the lines of "personal space", which is more of an abstract sense of distance and respect, it might be better to say something like "maybe people from different countries have different ideas of personal space".