Microchannel plate photodetectors provide both picosecond time resolution and sub-millimeter position resolution, making them attractive photosensors for particle identification detectors of a future U.S. Electron Ion Collider. We have tested the rate capability and magnetic field tolerance of 6$times$6 cm$^{2}$ microchannel plate photodetectors fabricated at Argonne National Laboratory. The microchannel plate photodetector is designed as a low-cost all-glass vacuum package with a chevron pair stack of next-generation microchannel plates functionalized by atomic layer deposition. The rate capability test was performed using Fermilabs 120 GeV primary proton beam, and the magnetic field tolerance test was performed using a solenoid magnetic with tunable magnetic field strength up to 4 Tesla. The measured gain of the microchannel plate photodetector is stable up to 75 kHz/cm$^{2}$, and varies depending on the applied magnetic field strength and the rotation angle relative to the magnetic field direction.