Why does Stockfish change its mind on what evaluation it gives the same move?

When I review my games, I will check my opening to see how Stockfish rates my moves.  For example, on my 3rd move, it will give me a 0.3 point advantage.  Then when I look at the exact same position again a minute later, it will have a completely different point advantage, sometimes even negative.  Why does it do this, and how can we trust anything that it evaluates?  

Your results depend on whether or not Stockfish is using your computer to do the analysis or if it using the Chess.com servers. And then again, the results depend on how long you let the computers run and how deep their calculations go. It is not surprising that the answers come out differently given those differences.

In general, people usually avoid using computer evaluations on the very early opening moves because there are so many possibilities available. Even the best computers have a hard time making sensible evaluations in such situations.

I am not sure if it is using my computer or doing it itself. Whatever it is doing, I would think it is the same each time, but I am not sure. And as for the time I wait, I always about a minute until the evaluation score quits changing. It seems to always quit at about 2 minutes or so. Everything that I do seems to be the exact same, but the score usually changes.

Engines will give more precise analysis of a position with the more time you give it. Engines can change their mind as they process more lines and possibilities. If you want it to be real accurate, you have to leave it for a while.