> whether or not others are required to use strong passwords has no impact on your privacy.
It's worth considering, though, that attackers may target sites that don't mandate strong passwords, because the password hashes in the site's database are likely to be easier to crack (and users with simple passwords are likely to reuse those passwords).
Once an attacker has chosen to target that site, that increases the chances that they find themselves able to read your data regardless of the password you used, because they'll have access to the whole database.
In fact, a site which hasn't put the engineering effort into enforcing strong passwords (not even a simple regex, let alone more complex approaches like checking for compromised passwords against the haveibeenpwned database) is also likely to have undervalued security in other areas, again making them a target.