So I have 1.5" XPS with 3/4" 1x4 furring. I ran furring around the top and sides of the sliders and am wondering how to furr, mount the slider doors properly. I am debating cutting out some furring and putting in a 1x4 (1.5 in thick) across the bottom edge so the sliding doors don't "hang" out. with a furring strip screwed to the 1x4 directly. Is the 1.5XPS with a furring strip stable enough for a big heavy slider door?

No, so set the door as an "innie". In other words, set the door to the inside of the wall, where it will bear on solid ground. You'll need to flash it well, especially around the bottom, use a good pan, and you can find alluminum threshold extensions online, or they may be able to build the door that way.

Door was ordered two,weeks,ago. Can't change the build of,the door. I already furred around three sides. Would there be a problem putting a 2x4 along the bottom edge (cutting away the foam)?

Fasten it well, since there will be a substantial load on it. Install a larger piece if you can. Either has to be pressure treated.

Are the wndows going to be ok? It was recommended on this forum to bring the foam up to the RO edge and use the fur ring screwed through. I originally was going to frame the windows with 2x4s...sheesh, I hope the windows are fine. So.e are 5 feet by 5 feet. Not as big as a slider. I assume most of the window load will be sitting on the 2x6s used as the lower plate of the RO...