As reported in this forum issue:

https://community.sparkfun.com/t/multiple-sparkfun-micro-oled-display/66302

I can replicate the OP's issue: with two 0.96" OLEDs on an ESP32 Thing Plus C.

Using the SPI Hello example, whichever OLED is begun first displays the splash screen successfully. The second is blank.

I spotted that the screenmemory is global (Link), but moving it into the class didn't solve the issue.