I was under the impression that even though a woman who had a real(halachic) conversion was not an Israelite, her children would be full fledged Israelites in every respect, indistinguishable in matters of Torah Law from those Israelites who are not descended from converts.
But the Mishna in Horayos 3:8 says that an Israelite takes precedence over a Natin. (A Natin is a descendent of the Gibeonites who converted in previous generations).
Now I know that as we don't know who is a Natin in this generation, any Jew who is not a Kohen or a Levi is an Israelite.
But does the above mentioned Mishna prove that the children of converts are not Israelites?