There’s a contraction between philosophy of building a MVP and being a fast follower. If the market is already tested and you have a feature that will enhance user experience or it is your product's unique value proposition aren't you running the risk of releasing it your competitors?
Yep. Although I don't think that's limited to MVPs. It's just always the case.
You can copy code, features, etc. but you can't copy soul. There will always be people who copy you. It's better to keep moving forward and accept the copy cats than it would be to try and shield yourself.
Keep an eye on the copy cats. But in the long run, if you're authentic and worthy, you will beat them.
It's really about how you and your team are different in the end. Yes, there is always that risk...it is just how things work in the startup world. No one is signing NDAs and your enhanced feature has likely been thought of by others. It is better to try and get your product / feature out into the world than hold it for fear of being poached by the big guys....they likely have bigger problems and opportunities to worry about. Take reasonable precautions and go for it.