As a man, who is six feet tall, I can say "Were I a woman, I would be less than six feet tall" and have it mean something. It is a prediction of how the world might be different if we changed one thing. This is what logicians mean when they discuss an alternate world.
I can say "If I am a woman, I am less than six feet tall", and it is nominally true, because the condition is false, but not in a way that means anything. I could equally say "If I am a woman, the moon is made of green cheese." and it would be equally meaningful.
However, saying "Were I a woman, the moon would be made of green cheese" indicates the two things are related for some reason and that my gender would be likely to actually affect the substance of the moon, which is nonsense.
So changing the mood here changes the statement from true but pointless, to theoretical and highly unlikely.
[This is hard to keep track of because the English subjunctive looks too much like the past tense, and people just fail to use it most of the time, or they use the past tense instead. Folks often say "If I was there", when they mean "If I were there".]
Also, there are variants of "would" that slightly alter the kind of alternate world the sentence is indicating. For instance, if I said 'might' instead of 'would', it indicates that the difference would not be logically implied by the change in the world, but would make it possible. "If I were a woman, I might wear pink more." means that my being a woman would make that possible. It would not necessarily happen, but it surely is not going to happen as long as I am a man. If I said 'should' it would imply things would be disapproved of in the alternate world because of social convention or moral sense, rather than actually being different. "If I were a woman, I should wear a shirt." But as I am a man, and it is 80F, I have mine off and no one cares.
[Again, hard to learn, because these are rules many people just fail to follow. The precise intentions behind words like might, may, should, etc. drift around a lot because they are poorly used. It is so bad that when it is necessary to insist they be used correctly, for instance in military specifications, people insist that their definitions be stated, even though they are being used with their traditional meanings.]
Logic models this as if all of the possible worlds created by changes to this one already exist, and we are just picking which ones to imagine working in. This is in principle silly, but it gives a clear way of discussing alternatives.
You can imagine that every counterfactual conditional is true in some alternate world. In impossible worlds, everything is true and false at the same time, and in possible worlds, the counterfactuals that are really true have true conclusions.
The problem is that the subjunctive places the statement in the realm of alternate realities and not actual reality, and without specifying which possible world you are talking about, the statement becomes true but useless. We need to know what kinds of rules we imagine are not changing when we change the thing we have chosen to change. Only the worlds that change what we intended and do not change the rest are allowed in an interpretation.
In situations where the range of allowed possible worlds is well-defined, either explicitly or by context, the subjunctive form becomes declarative when combined with that definition included in the premises. So suppose we said "Because of basic biology, if my other genes did not change, if I were a woman, I would be less than six feet tall." Then I can tell what is to be kept fixed when I consider the alternate gender, and only padded out in this way does the sentence have real and definite logical content.
Generally, we can guess what the omitted premises are, and we just don't say them. But if we cannot guess them, we just have to act as if the false conditions are meant to be taken literally, and the statement is just true but meaningless.
With this interpretation, the same is true of statements of obligation, those 'should' constructions, and of statements of mere potential, those 'might' constructions. They are all true all the time, but only meaningful with additional premises.