I guess two conflicting human rights I can think of are:
Article 18.
- Everyone has the right to freedom of thought, conscience and religion; this right includes freedom to change his religion or belief, and freedom, either alone or in community with others and in public or private, to manifest his religion or belief in teaching, practice, worship and observance.
and
Article 7.
- All are equal before the law and are entitled without any discrimination to equal protection of the law. All are entitled to equal protection against any discrimination in violation of this Declaration and against any incitement to such discrimination.
And for example in those cases I think that whilst religious people should be allowed to believe what they want, they shouldn't be able to discriminate against people unless it's for a role in that specific religion. So for example Catholic adoption agencies shouldn't be able to discriminate based on the sexualities of prospective parents, but would be allowed to discriminate on the appointment of priests.