Actually a consistently logical person _can_ be moral while declining to belive in something that has no empirical proof of existing.
Where will we find a 'consistently logical' person...and who will judge perfectly whether or not this 'found one' is consistently logical..against what perfect ground shall we judge him.. let alone whether or not 'a proof' is empirical?
Who cares if we have a perfectly straight line if it is going in the wrong direction?