How are you routing the power to (A) the MKR and (B) the display and what is the current / supply capability rating on each ?
Also bear in mind that the level shifter is DIGITAL ONLY and does not up or downshift analog voltages.
Its primary use is SIGNAL level shifting and NOT power. This could well be an issue if you mistake its capability.
That is the reason I suggested seperate PSU's for each.
So I think its back to getting a schematic.