What happens if you (try to) cast Catapult on an immovable rod? Which ability/effect trumps the other?
If the Immovable Rod is not fixed in place, worn or carried, Catapult will fling it like any other object weighing 1 to 5 pounds. If the Immovable Rod is fixed in place, Catapult will fail.
The whole point of Immovable Rod is to be magically fixed in place and immovable (well, resisting up to 8,000lbs of force). If a 1st level Transmutation spell can overcome this, then the magical item would be pretty worthless.
Common sense says it won't work, but a literal interpretation of the rules actually says it would work.
Choose one object weighing 1 to 5 pounds within range that isn't being worn or carried. [...] the maximum weight of objects that you can target with this spell increases by 5 pounds [...] for each slot level above 1st.
This implies that Catapult only exerts enough force to lift objects of up to 45 pounds (if cast from a 9th level slot)
An immovable rod
can hold up to 8,000 pounds of weight.
So catapult doesn't appear to be strong enough to move the fixated rod.
But if you are a rules-lawyer who insists on a very literal interpretation of all rules, you could point out that the immovable rod only holds up to 8,000 pounds of weight, while the catapult spell refers to the weight of the object itself. While the immovable rod is able to exert a large amount of force, it itself doesn't have a mass over 5 pounds, so it should be affected by it.
If someone brings Newton into the discussion and claims that mass is nothing but the ability to resist accelerating forces, someone else will counter with bringing in Einstein and claiming that mass is how much it bends space (which it apparently doesn't) and then someone reasonable will stop that by pointing out that DnD magic doesn't adhere to real-world physics and trying to argument based on the assumption that it does will break the game completely, so don't even start going down that road.
A counter-argument could be that the Catapult spell also says:
stopping early if it impacts against a solid surface
which implies that the Catapult spell can not exert a large amount of force. But the rule-lawyer will again say that the immovable rod doesn't impact a solid surface, so this clause doesn't apply.
So the literal rules-as-written interpretation of what would happen would be that the immovable rod is moved up to 90 feet in a straight line and then stays in place there.
The rod would not deactivate, because it only does that when its weight capacity is exceeded, and we just established that this is not what's happening in this case (it doesn't deactivate if moved with a strength-check either).
So how should a DM rule in this case? I would recommend to invoke rule 0. When in doubt, do whatever makes for the better story. Is it a cool idea which advances the plot? Allow it. Does it break the game? Disallow it.