If you own the domain being used, I assume you also host your own email… You can’t just make a new address for this and have them all forwarded to your actual email?
“This_is_not_generic” @ “your actual name”
Unless they block that too, I don’t think they’re trying to force those services on you; they’re just popular options and this is an automated response sent by an automated process that only checks the first half of the email and not the domain.