A rather long first post, I didn't finish it.
He may or may not be ok re texting others, but as it upsets you, one would have thought there would have been some form of compromise agreed from that discussion.
However as he admits to not being overly committed then you should be seriously considering whether you have a future with him.
I'm not going to tell you what to do because many fail to distinguish between orders and advice, but you should ask yourself if the relationship makes you happy, and will continue to do so in the future, before making any decision.