In the case of the dating site, someone who identifies as agender would probably not want to list themselves as male or female since they aren’t male or female, so they don’t want to attract people who are looking for only males or females. They could certainly list which genders they’re interested in dating, so they don’t get replies from people they’re not attracted to.
In the case of the job listing, I don’t think it’s legal to refuse to hire someone based on their gender? The only exception I can think of is perhaps in the case of acting roles? The actor could use their own judgement to determine whether it’s appropriate for them to play the listed role, and choose to apply or not apply based on that. I know multiple assigned-female-at-birth actors who regularly play male roles. They look androgynous enough to pull it off, and theaters are happy to cast them.