> Their "perception" is mistaken in this case.

It’s their right to decide how they perceive being approached by a stranger. And most of society is going to empathize with them and their feeling of unsafety, not with the stranger approaching them.

> even in your culture, public conversations significantly decreased in the past 30 years

The culture in my country never really had many “public conversations” from one stranger to another. This is something that has been noted by foreign travelers for generations now, at least back to the nineteenth or eighteenth centuries. What has changed are that the substantial family and institutional bonds I mentioned earlier have declined.

> do you think that gyms in your culture work differently?

They definitely do. This has already been mentioned by various people from different countries in this thread.