תמנע
The end of פרשת וישלח, talks about the families of Eisav. This shows the huge contrast between Yakov’s family that remained pure, and Eisav’s family that had many instances of incest.
There is a brief mention of a woman named תמנע. We are told that she was a concubine to Eliphaz, the son of Eisav. She gave birth to none other than Amalek.
The Gemara in סנהדרין says that Timna was a princess who approached Avraham Avinu with the intention of converting to Judaism. Avraham made a serious error by rejecting her. He felt she was insincere and had ulterior motives that were not pure. Because of this error in judgement, we ended up with Amalek.
The Gemara continues and tells the story of a non-Jew who went to Hillel. He said he wanted to convert on condition that he be made the כהן גדול. Hillel accepted him and he proved to be a good, G-d fearing Jew.
This illustrates that the conversion issue is not simple at all. Even Avraham Avinu misjudged a potentially good convert.