Unfortunately, CFExpress will probably require new readers (for the most part - there are a couple of odd ways that some might work). The good news is that, without the Sony monopoly, readers probably won't be as expensive (and, eventually, may show up built into other things, whether computers, docking stations, portable storage or simply multi-format readers).
There are actually three different devices that one might call an "XQD reader", and I'm not sure whether all will be incompatible with CFExpress. One is a true XQD reader - it connects to the PCIe bus on the card like the camera does, and it has a bridge chip from PCIe to USB (or potentially something else - but every reader I've seen is some flavor of USB 3.x). The second is a remarkably simple device, but it relies on some other form of PCIe bus being available. There is a Sony adapter from XQD to ExpressCard/SxS that simply connects the appropriate pins directly on the PCIe bus since both XQD and ExpressCard are actually PCIe - all it's doing is adapting the form factor. It should be possible (but I've never seen one) to make a simple adapter like this for XQD or CFExpress to Thunderbolt as well... The third variety is "USB adapters". Some XQD cards, but not all (for whatever reason) use some extra pins for a USB signal. A USB adapter connects to those pins and bypasses the PCIe signal entirely - it's just passing USB.
A true reader that is converting XQD to USB (or whatever else) would have some sort of firmware in it that would need to recognize what flavor of PCIe it was dealing with. Most card readers have that in a permanent ROM - it would be impossible to reprogram for the slightly different requirements of CFExpress without changing the chip. A CFExpress card reader could be built to know about both, or there could be some weird XQD reader out there that is firmware upgradeable.
PCIe adapters should work, at least in theory - we know the PCIe pinout is the same - that's why cameras are firmware upgradeable. Something that is simply extending those wires has no reason not to work unless it messes up timings or the like.
USB adapters should work IF CFExpress cards have the built-in USB "port" on them, AND it's on the same pins as it is on the XQD cards that have it. I don't know if either of those things is true.
In the end, anything with both an XQD and a SD slot (or pretty much any other second slot) on it is a true reader, and won't work unless it is firmware upgradeable. Something cheaper and single-slot that calls itself a "USB adapter" may well just be connecting to the USB port on some XQD cards, and could work if CFExpress has a USB port in the same place. An ExpressCard slot adapter (or anything else that's direct PCIe to PCIe) should work in theory.