Do you know why they quit their jobs? Is it depression? Is it dysphoria? Or is that they are just used to you picking up the pieces, so they quit jobs when they are unhappy?
I personally think that unless there is a significant psychological reason that they keep quitting their job and there isn't an agreement that only one of you needs to have consistent income, then you should expect that they hold onto a job until they have another one.
I like Dena's idea of putting out money for a blocker now if you can afford it. It could help with any depression that may be dysphoria related. When they get another job they can head back to therapy and get estrogen. I hear that them not doing therapy/estrogen now is about money, but I also think a bonus of the situation is that it could be helpful to their own process of being motivated to get and keep a job, if they have something they are working towards.
I like your idea of telling them in therapy that they need to hold onto one job before getting another if they want to move forward with things like surgery. It may help them from quitting jobs when frustrated. Obviously, therapy would also be a great place for them to figure out why they keep quitting jobs.
As an aside, I believe that it is suggested that people not go past 6 months on blockers alone for health reasons. So, if typically takes your spouse longer than 6 months to get their next job, they may want to delay starting the blocker. I imagine it would be quite emotionally damaging to have to go off of the blocker after having been on it. HRT is like nirvana for some of us. It would be worse for me to stop taking testosterone (I am FTM), then to have delayed longer to start it.
I personally think that even if you could cover all costs, you would be doing your spouse a disservice by paying for everything if they have the ability to participate in paying for it by working. Know that you are still being supportive even if you set a limit in this regard.