Three characteristics would be important in finding a replacement transistor, the SOA, threshold voltage, and the transconductance. The loop bandwidth for a linear power supply is most likely going to be low enough where the capacitance's of the MOSFET will not impact any of the major poles/zeros that are important for control loop stability, so unless there is an order of magnitude difference you can probably ignore matching that.
At a maximum current of 6A the sharing resistor is only going to drop 0.44V per part, and less that that at lower currents. The threshold voltage is not typically specified this tightly in datasheets. Ideally the three transistors would be the same part number from the same manufacturing lot. It would be hard to get a replacement part matching the threshold voltage within the ~0.2V or so required to effectively share power given the value of the current sharing resistor.
Loop stability is going to be impacted by transconductance, which determines the gain (ratio of drain current to gate voltage). In order to switch faster, modern MOSFETs often have a higher transconductance. Even if the threshold voltage of a replacement part was the same it may not share current equally due to a different transconductance. Transconductance is often given at a single current which can be different between datasheets, but scales with the square root of drain current, so parts can be compared. The current sharing resistors provide negative feedback and reduce the impact of the transconductance. As transconductance increases with drain current any stability issues will happen at the maximum load current.
Due to variations in threshold voltage I would recommend replacing all three transistors together, ideally with parts from the same lot. Control loops are generally tuned with enough phase margin where even a multiplicative increase in the loop gain should still be stable (notice that the BUK436-100A does not even specify a maximum transconductance!).
I recently fixed an Agilent linear power supply that used a IRFP150N so I am fimilar with the part. Looking at the datasheet it has almost the same transconductance as the BUK436-100A.
https://www.digikey.com/en/products/detail/infineon-technologies/IRFP150NPBF/811534 It seems like the part should work in your application. However, it technically does not have a DC SOA curve.