But even so, many times a website seems to ask for data they absolutely strictly don't need. Electronics shop -> doesn't need my gender, nor birth date really.

If someone does need my birth date, they typically a) don't need to store it but just verify, and b) what they'd really need would be a trusted third party (like my govt ID) certifying that date. And even then, often just properties about it like "is over 21" or such. Which is incidentally what my german ID allows to do, albeit in a way too complicated way.