Besides “your password must contain this” complexity requirements, some places also have “your password must not contain this” rules, sometimes with fairly short substrings of the username, a day of the week,… being enough for a password to be blocked. For a password strategy that theoretically could generate any string, this might still leave a reasonably large amount of possible outcomes. But what happens when one uses Diceware to generate passwords, and the rules completely rule out certain words (or combinations of words, if e.g. your passphrase contains “mushroom online” and the password checker decides clearly this is because it’s your password for Mondays and that’s unsafe) - can such rules reduce the amount of possible passphrases enough one would need another strategy for such sites?
TLDR: Yes. Depending on constraints the number of allowed Diceware passwords can be very small and brute-forcing can be easy. It depends on particular constraints.
Every approach has its applicability. Diceware is not a universal approach and can work well under certain conditions only. The answer on your question depends on how many potential passwords are prohibited.
A password consisting of 7 English Diceware words has entropy of 90,5 bits. If a small part is prohibited, let say 100 out of 7776 words, then the passwords will have entropy of 90,3 bits. For brute-forcing it is very small difference.
But if the most Diceware words are prohibited and only 100 words are allowed, then a password of 7 words will have entropy of just 46,5 bits. This will essentially reduce the resources needed for brute-forcing.
Computation of effects of other rules like in your example can be not so trivial. But the approach is the same: Compute entropy and decide if it is acceptable. Also check if adding 1-2 words can give you the desired entropy despite constraints.
There can be constraints that make usage of Diceware impossible. For instance, if the application prohibits any dictionary words, then usage of Diceware is impossible. Some applications limit the maximal length, and it can be extremely small, e.g. not longer than 15 characters. For passwords consisting of random characters the entropy can still be high, about 90 bits. But for Diceware this will limit password to 3 words and thus the entropy to just 39 bits.
An alternative can be the usage of a password manager that has no restrictions for Diceware. Use Diceware password to secure the password manager. Then generate randomly passwords for applications using their constraints.