Someone with a BTL (Bachelor of Talmudic Law, the yeshiva “degree”), or for that matter a conventional B.A. in Jewish studies, or for that matter any degree in the humanities (other than history) or sciences — will be at a disadvantage when they get to law school.
While it is NOT required for admission, it is very helpful to have a basic knowledge of history (particularly American and to a lesser extent British) and social sciences are very useful, writing and communication skills are critical. If a student is good enough to get into Harvard or Columbia, or even to Brooklyn Law School or SUNY-Buffalo or University of Baltimore, or even good enough to pass the first year and read law – the student probably has the ability to sit down and read up on the subjects they are weak and work on the skills they need.
Even if someone with a weird background is looked down upon on the first day, very quickly what will matter is whether they can hold their own with the rest of the class and the profession.