If my church says they support me in doing missions but won't financially support me when they are able, should I find a new church home?
I would say it depends on why they are not.
It sounds bleak to me: they are able; they say they support you; you sense a call from that body; and they don't add to that prayer support or whatever it is—money.
My next step would be to say to the powers that be, "Why?" And then judge on the basis of the answer whether there is a disconnect here.
They might say, "Well, you are a son of the church and so we like the fact that you are going to missions, but your theology has taken a turn we are not comfortable with." That would then be the issue, not they won't give me money.
So my answer is, find out the issue and then let that be the issue you deal with, not just the money.