Reddit reviews Deuteronomy (The Expositor's Bible Commentary)

Scholars Christopher Wright and Michael Grasanti state this is referring to those who were born from rebellion (the intermarrying of the Israelite people and pagans), incest, temple prostitutes, adultery, and any other unlawful sexual relationship.
To allow these children to attend would be to snub your nose at the Law and commands of God. It would be almost as though they were boasting in their rebellion. It is further thought that if one is participating in this kind of relationship, the parent is also guilty and would be cut off from the assembly.
The tenth generation, according to Grasanti, is a permanent ban to be enacted on unrepentant sinners. This suggests that if one born of an illicit union was to place themselves under the Law and worship YAHWEH alone, they could join the assembly.
Sources:
Christopher Wright - Understanding the Bible Commentary
Michael Grasanti - The Expositor's Bible Commentary
edit - typo