Are theories always either true or false?

In practice, no.   In principle, perhaps the answer is “yes”, but if so they’re probably all false.

The classic example is Einstein’s Relativity theory [1, 2, 3].  Relativity is correct (so far as we know), and it has replaced Newton’s theory [1, 2, 3] in terms of how we think the Universe works.  But Newton’s theory is perfectly good for all practical applications on the surface of the Earth.  It is almost correct.

One would have to be a pedantic sourpuss to call Newton’s theory “wrong”, because it’s actually rather hard to set up an experiment where it produces a noticeably wrong answer.  (I.e. you probably can’t do it for less than $1 million, unless you do something clever that uses the GPS satellites.)  So, in the practical sense, Newton is only slightly wrong.  Einstein’s theory may be imperfect too, but would be even closer to being right.  (I.e. even after someone figures out an experiment where Einstein’s theory might give the wrong answer, it’ll probably cost a billion dollars to do that experiment.)  In fact, we think there are at least 50-50 odds that Einstein’s theory is wrong because it appears to conflict with our other nearly-perfect theory in physics, Quantum Mechanics.  If they conflict, one or the other (or both) must be imperfect.

 If you had really asked this question, your problem would be that you wanted to use the terms “true” and “false” — which are really terms from mathematics and logic — in the real world.

In the real world, the correct questions to ask are “is this accurate enough?” or “will my airplane fly?” or “does it help me understand what is going on?”  In the real world, you will never have a perfect prediction, because you always need to simplify the world before you can apply a theory to it. So, if you insist on being a logician, no prediction is ever quite true, because you can never quite fulfill the assumptions of your theory.  Even predictions from a perfect theory would be imperfect because you cannot describe the world precisely when you try to apply the theory to it.  Nonetheless, science can often give us predictions that are amazingly precise. We thus have theories that are incredibly useful and provide beautiful explanations. [And they let our airplanes fly.] But it doesn’t make sense to ask if they are ‘true’ in the sense of mathematical truth; science uses a more pragmatic kind of truth.