It is not a loop

All these explanations I read, miss two very crucial things.

First, that time agency exists and does things. If time would be fixed and unchangeable, they could not do anything, it would all be predestined.

Second, they say the fizzle bomber keeps changing the date of the big explosion.

So there must be a time line where the bad things happen, that they prevent. They can go there or live through it and take things like newspaper cut outs back.

What this means, is, there is no closed loop leading in itself. It only apparantly leads into itself, but it can change. It is like a spiral when viewed from a above. It looks like a circle, but is not a circle.

So there was a first timeline pass where the machine was invented, and they started travelling back to change things after the fact. With each travelling back, a new line of time was created, with new outcomes of events and possible different bad events that they would want to change.

The events in the movie represent one pass in one spiral and the changed bombing event date indicates that it is in fact not a same circle loop. So there was a first big bombing and trying to prevent it did not work, but changed the date. And this several times.

Likewise there was a first pass, where John was not his own parents. Maybe they recruited a regular Jane and the time agency boss set events in motion, with the help of some hormones, to make Jane0 pregnant with some astronaut to give birth to Jane1, a functional internal hermaphrodite. Jane1 would be sent back in time where she could be recruited again to now be impregnated by John1, a time travelling and gender changed Jane1. Resulting in Jane2. The person would change slightly with each generation, but the limited gene pool would stabilize results. As a sick bonus they would let handle JohnN the creation of JaneN+1.

That boss talked about doing things outside the rules, so he possibly not only created some of his agents, but also started to manipulate John to change some events that previosly could not be changed, because it would have required to kill large groups of people.

So to answer the ending, did JohnM break the loop? Since it is not a loop, maybe. Maybe not. It depends entirely on the time agency and if their work is done. If they changed all the bad events there will be a pass of the spiral where they do not travel back and the time line passes past the point of possible travel. So if the fizzle bomber is still needed, the agency boss would just manipulate JohnM again. Or JohnM+1. We see a lot of tape recordings being used. This way John could easily be manipulated.

But since JohnM did recrute JohnM+1, there still seems work to do.