Actually, I have only heard the opposite - it's a great miztvah to adopt a
Jewish child because, as Akiva says later, we should take care of Jewish
orphans as much as possible. The problem actually is that there aren't
many Jewish babies put up for adoption, certainly not as many as potential
Jewish adoptive parents.
The one issue I have heard of regarding adoption of Jewish children is
mamzeirut (illegitimacy). If the child was conceived through an adulterous
relationship, then the child would be forbidden to many other Jews. I
think that adoptive parents investigate this possibility first. If there
were such a problem, my guess is that it would be beneficial to obscure the
child's background so that he/she would not be subjected to difficulty
marrying with such a status.