This is not a Christian family, this is a deeply misguided family who are distant from God.
Notice the logic here. The father looked up the condemnation of sodomy in Leviticus and noticed that the consumption of shellfish is also prohibited. He then concluded that since he felt shellfish were okay to eat, that sodomy was totally okay too.
If he had been even a foolish Christian, he would have read the passage and repented for his last meal at RedLobster. Had he been a vaguely well-versed Christian, he would have understood civil law as applicable to Ancient Israel, and the moral law which is binding on humanity until Judgement Day.
The fact that his conclusion was that same-sex activity was permissible based on shellfish shows us that this is no more a Christian than Bill Nye is a scientist.
It looks like the family was already attending a PCUSA(a denomination that already supports abortions and female elders as well as allowing ministers who deny things like the virgin birth, the resurrection and the infallibility of the Bible) so I think they lacked discernment skills long prior to this issue with the son.
These people are not only using poor logic they are misleading and possibly leading others astray. They need bible 101 and need to read it in context.