There may not be a conflict. Chances are good that if no problems have ever arisen to lead you to believe there's a conflict, and if Windows runs fine and you can use both hard drives without trouble, then there's no conflict.
You'd need to be more specific about this "system info type screen" you're looking at, and exactly what it reads; but possibly if your motherboard has two IDE connectors, and one HDD is connected to each of the connectors, then one HDD might be called 0.0 and the other might be called 1.0 -- making it look like they are both 0, which they technically are except that one of them is HDD-0 on one controller, and the other, is HDD-0 on the second controller.
As for whether or not there are any motherboards that are particularly bad for Linux? Generally speaking, no, pretty much any motherboard should be fine. HOWEVER: historically speaking, there *have* been a few situations where a piece of hardware, such as a disk controller, have required firmware to be installed onto them before they would work right. This has been exceedingly rare, and I can't even recall the last make+model of a motherboard where that happened. Otherwise, while pretty much any motherboard will work, it's a good idea (particularly before purchasing a new one) to investigate exactly what hardware components are built onto the board. Things like NIC devices (networking controllers, wireless devices), RAID chips, and certain video cards, can have varying degrees of compatibility & functionality when powered by Linux.
Again, *generally speaking*, most motherboards will work with good or great success. A rare few will cause bad problems, but which can often be solved or worked around, with a bit of perseverance.