There are many statements we would agree to be neither true nor false; here are a couple:
1. The sun will rise tomorrow. 2. This statement is false.
Note that this is not the kind of information which is controversial in our society and germane to decision making. (Other than that we will assume the sun will rise tomorrow as a given, but we can't stop with that.)
If you're going be that pedantic, you rule out all statements of moral or value judgement, all statements pertaining to the future, and most things relating to abstract nouns. This makes it impossible to discuss anything political at all.
Then they're not valid for anyone else who doesn't have exactly the same set of axioms. You can only form sentences of the form "I believe it is wrong for me to ..." and not "I believe it is wrong for you to ..."
wyager either doesn't want to construct such a logical language system and is just pedant-trolling us, or he's too naive about the underlying inconsistency of human languages to bother talking to.
1. The sun will rise tomorrow. 2. This statement is false.
I'd agree with you the validity of a statement is not dependent on the palatability of its consequences.