For Bitcoin, whenever the repository owner pushes changes, the miners approve or reject them. That takes away the central control. But since IOTA doesn't have miners, what's the process of making changes to IOTA? Is the entire control with the repository owners? What am I missing?
There is no miners on the tangle but they are individuals running fullnodes. They are free to run their preferred implementation of the protocol.
So if you fork the IRI and are able to convince the community that your implementation performs better... in theory it can be adopted. This is not fundamentally different that what's drive the bitcoin community (except that individuals running fullnodes don't receive financial incentive).
Note that today, the coordinator plays an important role on the tangle and is not open source, but in the end, the coordinator will be removed and the protocol will be fully open-source.