The R2000
Umm, the SONY Playstation1's CPU is a good example of MIPS design where you can set the endianness. SONY went for LE, the firmware is LE, and every game ever developed is LE.
I am more interested in MIPS32r2 and MIPS64r2. Although nowadays MIPS are usually used for router products, a few companies located in China have already designed ATX motherboards for daily computing needs, and usually, you can't set its endianness by setting a bit during the early bootstrapping. It's hardcoded, thus you have to consider their products as LE machines.
Concerning linux, there is kernel support for LE<--> BE. Even if some kernel-driver are still bugged due to the endianness