I'm not too worried about hostile responses, with my history of being antagonistic towards religion. However, I don't mean any disrespect in this instance, I'm just trying to provoke thought and discussion. I would also like to understand better how people square the Old Testament with the New Testament, which I personally find to be stark in their contradictions. The OT God has characteristics that are not present in Jesus.
I think you are conflating two unrelated things here.
No theology I've ever heard of claims that the differences between the OT and NT are the result of God changing his mind.
So, you have two separate questions here:
1. Can God change his mind?
2. Why is there such a difference between God's commands in the Old Testament and the New Testament?
I'm going to leave question 1 alone because that leads into a number of rabbit holes I don't care to jump into in an environment like this one.
Question 2 has a more straight forward answer that is more fitting for this kind of forum. Basically, God chose to reveal himself within history and to play out his rescue plan within history. His plan has several phases. Some of those phases are over. The phase we are in now is different from the phase people were in prior to the arrival, death, and resurrection of Jesus. The laws of the Old Testament were necessary for that stage in the journey, that phase of the rescue plan. After Jesus' death and resurrection tore the veil and made the holy spirit available to everyone, a new stage in God's redemptive plan began which made many of the Old Testament laws unnecessary.
Imagine you were on a journey (I'm stealing this metaphor from N.T. Wright). The first part of your journey was by boat, but you have now left the boat and are on the last leg of the journey, which is by land. There are many rules and traditions that made sense while you were traveling by boat. Perhaps when traveling by boat you needed to keep certain hours in order to take best advantage of the wind. Perhaps while on a boat it was best not to have any pets since getting rid of their waste was a problem. Maybe while on the boat half the people had to be awake while the other half slept because the limited space on the boat meant everyone shares the bed (hot racking). But now your journey is by land and the rules are different. Perhaps now the hours you should keep are different; maybe it's ok to have pets now, maybe it's ok if everyone sleeps at the same time, etc. It's not that the rules and traditions that were in place while you were on the boat were wrong all along and you should never have done things that way. It's that they were right for that period of time, but we have moved on to a different stage in the journey and those rules no longer make sense for this stage.
Therein lies the difference between the rules we see God giving people in the Old Testament and what we see him giving people in the New Testament. Jesus' life, death, and resurrection ended the previous phase of God's redemptive plan and ushered in a new age. It's not that everything that came before was wrong, it's that it is no longer necessary. Jesus has arrived and the holy spirit has been made available to everyone. No longer is the holy spirit a presence only one person gets to experience on a single day of every year; it is now something that is available to every person at all times. That changed everything.