As the school mentioned, for the kind of counseling program in question, the students are being prepared to work in agencies that do not necessarily have the capacity for referrals.
The university has no say in where a student will eventually work after graduation - or even if a student will choose to work in the field or not.
Such choices are for the individual student to make.
It is the job of the university to teach a particular subject matter - not dictate opinion and belief onto the students.
Referral for specialization is different from systematic exclusion of clients.
Not if the systematic exclusion is for particular disorders.
To not treat clients presenting a particular condition - and referring them elsewhere instead is a perfectly acceptable practice in all professions that come to mind.
And, no, I would not argue the same for a medical student in that scenario. No ethical code or demand of the profession requires that a doctor perform abortions.
And no ethical code or demand of the profession requires that counselors, psychiatrists or psychologists treat every and all patients that present themselves.
An initial client interview to determine whether or not to accept a particular client is the norm in most professions.
When I was practicing as a CPA I accepted about one client in three.
I had various reasons for not accepting clients - but my reasons did not matter - I was free to accept or decline new clients as I saw fit.
Counselors have no ethical or professional obligation to accept every client either.