If I had 2 really strong magnets, and I threw one into a black hole, while holding one outisde it at a safe distance, what would happen? Would the magnets affect each other in any way? Would one push/pull the other?
The tidal forces emerging from the black hole would at first break the magnet flung towards it into two pieces. Those two pieces would themselves undergo deformation and splitting, as the process of spaghettification will continue beyond the molecular, atomic and even sub-atomic levels, reducing everything that crosses the Event Horizon to a Singularity.
You won't actually see the magnet thrown towards the black hole crossing the event horizon, but that's a different matter altogether - please see this if it might interest you.
Now, magnetic attraction is essentially just an Electromagnetic Force, the range (not to be misunderstood as strength) of which is infinite - see reference.
In the context of the scenario stated in the question, the fate of attraction between a pair of magnets, one of which is thrown into a black hole, could be visualised by the following analogy: imagine holding a magnet in your hand and the other attached to a train which is accelerating downhill into a gorge. The two possible results are:
If the attraction is strong enough to pull the magnets together before the train falls into the gorge, then they both crash into the abyss together (assuming that the magnet attached to the train would easily be able to pull the one that's being held by hand). In case of a black hole, this would mean that both the objects (magnets) would be crushed to singularity. However, we might safely say that they both were "attached" before crossing the Event Horizon.
Or, the acceleration of the train reduces the attractive force infinitesimally, with the magnet in hand barely having any effect on the other magnet that crashed (and vice-versa). In a classical sense, this means that the force of attraction would still exist, even if it's reduced infinitesimally, to almost zero. However, with regards to a black hole, Event Horizon ensures that anything inside the horizon can no longer communicate with or influence anything outside the horizon (and vice-versa). This means, if the magnet somehow crosses the event horizon as a single piece, before losing its existence to singularity, its magnetic attraction would still never be able to cross the boundary defined by the horizon, even though the range of influence of the electromagnetic field is infinity. Ultimately, this would only last for a very brief moment and the magnet would be unable to prevent being pulverised to singularity, either by itself or by any attempts from any other entities outside of the Event Horizon.
Hope this helps.