Players operating out of turn

This would make the game more realistic. However, do you think it make it too complicated? People will inevitably forget which worker has done what. In theory, I could give each player a card where they can keep track of which worker has taken how many actions (dice maybe), but people may forget to keep track of it.

Another problem is that it slows the game down considerably. You have to keep having pauses to allow other player to do things, and you can't plan your turn ahead of time very well, because people may play a card half way through and force you to change all your plans.

A third problem is that unless you are careful, you get timing issues. Two player try to do something at once - which one gets to do it? A player plays an action, and then a second action. Another player claims that before the second action, they wanted to do something and didn't have the chance. Do you take back the action, or has that player missed it? What about taking two actions back. What about if the player does the second action very quickly to forstall any additional moves.

My conclusion would be that if the change is just to make things more realistic, then don't do it - you add a lot of complexity. If there are some gameplay benefits, then it's your call about whether they are worth the cost.