Reproduction steps:
1. Open the attached project "Repro" from the google drive link
2. Select the "AppliedLocalVariables" GameObject
3. In the Inspector window locate the "Local Variables" section and in the "Object Reference" field add the "Main Camera" GameObject
4. Select the "NotAppliedLocalVariables" GameObject and do the following like in step 3.
5. Enter Play Mode and notice that the "Object Reference" in the "NotAppliedLocalVariables" GameObject is the same
6. Inspect the "AppliedLocalVariables" GameObject in Play Mode

Expected result: "Object Reference" in the "AppliedLocalVariables" GameObject is "Main Camera"
Actual result: "Object Reference" in the "AppliedLocalVariables" GameObject is "None"

Reproducible with: 1.0.3, 1.0.5 (2021.2.5f1, 2022.1.0a16)
Not reproducible with: 1.0.5 (2022.1.0b1)
Could not test with: 1.0.5 (2019.4.33f1, 2020.3.25f1) (Various project errors when downgraded)

Notes:
-Leaving Play Mode results in the "Object Reference" to lose the specified GameObject and stays "None"