why should this a problem? Random is random and each rule you add reduces the "complexity". If I know, that it must not be the original birth date, there are 30 possible days in January, without this rule it could be within 31 days.
Same is true for passwords, if you allow only latin A-Z upper and lowercase, numbers and maybe 10 chars, the total amount of passwords is much lower than if you would allow every unicode char. And if someone wants to start his password with a 💩-smiley it is fine and much more unlikely to find in some password databases than password starting with a simple A .
God is real, unless declared integer.