Quantum theory is only "controversial" to the general public, mainly because we haven't found a way to explain in simple terms things like superposition, entanglement, quantum tunneling. Quantum theory is spectacularly successful, though incomplete.

Even the "simple" stuff like the uncertainty principle takes a detailed understanding to properly grasp why there are pairs of properties that are inherently linked, and that information about one dictates how much you can know about the other. e.g. position/momentum and energy/time.

You can transmit something, but it has a noise added to it. To decode it, you need to send the readings to the other end, via normal means. Basically, the receiver can tell, in hindsight, that a message was sent, but only once its other half has been received via normal means. The best you can do is get a timestamp of when the message was sent, as well as a message channel that is impossible to intercept.

The problem comes when QM meets relativity. With instant communication, you can send information into its own past. E.g. A and B are 2 planets. C is a ship, passing planet B at relativistic speeds. Planet A sends a message to B, over the FTL link. B then sends it to C, over a normal link. C, finally sends it back to A over FTL. Due to the 'tilt' of C's light cone, the "now" of A-C is behind the "now" of A-B. This allows for paradoxical situations. The maths of Relativity implies that you can't form a closed time loop like this. Such behaviours tend to imply some deeper rule, even if we haven't found its cause yet.

Quantum mechanics has a lot of strangeness. It also seems to play fast, but not loose with causality. E.g. objects can move backwards in time, but still obey causality. Others can be smeared over time space, but still collapse to a causality obeying state. Etc

I might be wrong, but iirc quantum theory just straight up doesn't give a shit about causality. Where everything else requires the cause to be observable before effect (something travelling faster than light would result in effect being potentially observed before cause), quantum theory says, "why does the universe give a fuck whether or not we can see it? If it happened, it happened, regardless of whether or not we observed cause before or after effect."

Well, yes. We don't know if the measurement we take is the result of a wave form collapse (we caused it) or the result of someone else having measured it, which would giving us the oposite value that they measured. We can't tell if someone "sent" information or if it was the random result and we have no way to chose what value we (or the other end) gets when we collapse it.

This isn't easy to explain over text so I'd recommend watching this video, specifically chapter "How to exploit?" as the visuals make it easier to understand.