I think that many people have aversions against elites seeking some form of immortality for themselves. Reproductive cloning would only enable a relatively weak for of immortality that might not be available to everyone. Therefore, some people could argue that reproductive cloning creates intolerable relative advantages for a relatively small group of people who can afford that procedure.

In the case that reproductive cloning could be afforded by virtually everyone people could still draw some kind of connection between cloning and incest, as both acts can be seen as diminishing genetic diversity. Less genetic diversity could decrease the overall level of immunity against diseases. But perhaps you could compensate for that with some genetic treatment before the implantation process.

Additionally, those who create a clone of themselves could be seen as egocentric, because they don't seem to be ready to mix their genetic material with someone else and prefer their own undiluted genetic code.