I am currently just saving info vars and strings everytime I exit my game. I then load them when I start the game. I read in the manual that if a game were to be saved with a different script than the one that is loading, there will be problems and a crash.

After I release my game, I plan to continue to update it's code with new updates. If a user installs the new update, would this make there save files invalid? If so, how would I go about making sure that everyone's saved progress loads from version to version? Because otherwise they will lose their progress and not want to update.

There won't be a crash, it just won't load. For saving vars and strings regardless of your script, use a text file.