As far as I know if a male is unable to have children due to body damage, he cannot become a ger. I have also heard of Beitei Din not allowing deaf people to convert since they cannot do certain mitzvos (e.g. they cannot say kaddish and certain prayers so conversion may be damaging for them, spiritually). But what about the general case - is it common for a Beis Din to reject a convert because of a physical disease (like cerebral palsy) or deformity?
Is there a halakhic prohibition against converting people with certain physical disabilities?