Where the reason for the early persecution of Valen's children ever given?
Was is biological? Was it because they appeared more human then Minbari - be it because Catherine Sakai did not undergo a full transformation, or their human genes were dominant?
Was it political? Did the Grey Council fear they would set themselves up as rulers over the Minbari?
JMS has not stated definitively why they were persecuted, but it is most likely because Valen's children were not full-Minbari.
The Minbari are largely homogeneous and isolated from other races, and many discriminate those who are not Minbari. In fact, Sinclair specifically says that he decided to become Valen because the Minbari would not accept Babylon 4 from a race other than their own.
If Valen had children with a full-Minbari, then his children would be 3/4-Minbari. It's possible that they exhibited some signs of being human, although since Valen was able to pass off as a full-Minbari, this is unclear. But if they had no telltale signs that they were human, and if word never got out that Valen wasn't full Minbari, nobody would ever know.
However, the 100% canon novel To Dream in the City of Sorrows (written by JMS' then wife) and the comic miniseries In Valen's Name (written by JMS himself) indicate that
Catherine Sakai was caught in a time rift in the Babylon 4 sector, and it appears she was sent back in time to the first Shadow War. Sinclair/Valen managed to find her and they seemed to be living happily together. Given that, it is reasonable to speculate that she might have been the mother of Valen's children. (More info on Catherine Sakai's fate)
If that is the case, then Valen's children are only 1/4-Minbari. At that point, it would likely have been more obvious that they were not truly Minbari.
It seems that all Minbari consider Valen to be full-Minbari (aside from those who know he was Sinclair), so the fact that he had children with a non-Minbari, and his children were "impure" likely led to their persecution. There may even be some sense of righteousness in destroying all remnants of Valen's one "indiscretion".
We know that Valen established the Grey Council, which appoints their members. However, Dukhat chose Delenn to be his aide, and eventually a Satai on the Grey Council, partly because she is a descendant of Valen. It is possible that this preferential treatment indicates that some Minbari viewed the children of Valen as having a special claim to leadership, potentially even the right to the same sort of unilateral rule their ancestor had.
This would parallel the two major branches of Islam: Sunni Islam believes that one who is chosen by the consensus of the Islam communities should be the rightful leader, whereas Shiite Islam believes that only those who can trace their lineage to Mohammad should be the rightful leaders.
Given that there are prophecies about the Grey Council continuing to exist for thousands of years, it would be reasonable to assume that if this viewpoint existed, there would be an effort to kill all of Valen's children in order to make it a moot point (no children can lead if they are all dead). If the children were only 1/4-Minbari as described above, then there is extremely likely that it would motivate ending this viewpoint, if it existed.
