She said that they should ban fraternization because it ruined morale and discipline, Chakotay countered with them needing a replacement crew come the half way mark, which was such a reasonable thing to say that she stopped talking without confirming that he wasn't wrong.
The Quakers at the end of the 19th century were a massive religious and political movement in America, however, unfortunately they banned sex even between married couples. They believed that they should only expand their ranks through adoptions. Which explains their near but extinction.
Surely by banning sex but between the same ranks, is the construction of a class system which is illegal under the federation by-laws? It's more than possible that such backward thinking bound into pro tem regulations is highly illegal and warrants a court-martial and dishonourable discharge.
Which is ironic.
Since all Kathryn is trying to do, is stop dishonourable discharges between her crew.