You can set the memory to 2666mhz on ANY board that supports that CPU. With a Z390 board you could POTENTIALLY set the memory speed to it's XMP profile of 3000mhz or whatever speed the memory is advertised to run at but I wouldn't try anything past 3000mhz since that CPU is not overclockable on ANY motherboard, and a CPU overclock may be likely needed to run at speeds higher than 3000mhz in order to wake up the internal memory controller.
Personally, I don't think it's worth the extra price of a Z series board for THAT processor, just to run at the higher memory speed however there are no lower chipsets that FOR SURE support that Coffee lake refresh processor out of the box without potentially needing a BIOS update so if you want guaranteed compatibility then Z390 is unfortunately the only chipset which is guaranteed to not need a BIOS update just to use that CPU.
If you get a B360 or H370 board, be sure to verify that it DOES in fact already have a BIOS version that supports the 9th gen Coffee lake refresh CPUs before purchasing otherwise you'd need an 8th gen CPU in order to get the BIOS updated.