Foil-faced iso like Tuff-R
IS a vapor barrier, which can be both good & bad, but in this case maybe good, but it depends. Is there's a cavity/gap between the brick face and the block wall? How are the floor/ceiling joists mounted to the block?
Mold & moisture problems are only created when moisture can get to the wood, but can't leave. Before insulating, air leaks and vapor diffusion through the gypsum on the interior reaches the cold block wall and condenses when the block is below the dew point of the interior air (typically 35-40F, depending on how warm & humid you keep it indoors), but the block can wick it in without damage, and releases it quickly when the block warms up. After insulating between the gypsum & block the block stays colder (much much colder), and as it's humidity rises, puts the furring and joist connections at risk. With a good air seal on the foam the volume of diffusion & air transported moisture is small, and if there's a vented cavity between the block and brick moisture will be released to the outdoors over time, even in winter. With a cavity-wall the overall performance would be enhanced with an interior vapor-barrier (like foil-facers on Tuff-R), but with a solid masonry wall moisture drives from the exterior during the spring/summer/fall could be much worse than the winter drives from the interior through 3/4" of XPS. While XPS allows more moisture into the block via vapor diffusion in winter, it allows several orders of magnitude better drying toward the interior. Since the block is mostly impervious to the wintertime moisture drives (unlike wood-sheathed buildings).
A typical brick-veneer CMU block wall comes in at a whopping ~R2-2.5 if uninsulated, and they leak air. If the block wall is hollow CMU you can typically double that by filling the hollows with a vapor permeable non-expanding injection foam such a
Core Fill or
Tripolymer. That would be step-1, bringing the wall's R value up to R4-5, which is only about half the R value of a typical 2x4 studwall with R13 batts, but WAY better than R2.
Then...
With a vent cavity between the walls you can safely add 3/4" foil-faced goods between the furring. Without it, use 3/4" XPS (pink or blue board) insulating sheathing, which is semi-permeable to water vapor to allow the block wall to dry toward the interior, lowering the risk to any wood in contact with the block. With either type of foam board you may still have to leave 6" clearances around joist ends to allow sufficient drying depending on how it's attached, but the overall risk is much lower in a cavity-wall than a solid type.
Cut the rigid foam for a loose fit and glue it to the masonry using blobs of foam board construction adhesive, and use 1-part can-foam (Dow Great Stuff, or similar) to seal the edges of the foam-board to the furring. Trim the can-foam flush with the furring with a knife or saw after the foam has cured.
Alternatively you could inject the same vapor-permable non-expanding foam into that mini-cavity as well as to the CMU cores, if the installer thinks they can do it all without stripping the gypsum off the studs. The vapor-diffusion would be about 5-10x as high through the injection foam as through XPS, so this would be best done on cavity-walls only, since cavity walls dry toward the exterior so much better.
With 3/4" of iso (Tuff-R) you'd be adding R4-5 to the center cavity R value, but only ~R3.5 to the whole-wall R value (whole-wall is with the thermal bridging of the furring & framing factored in.) With 3/4" of XPS (typically cheaper), you'd be only adding R3.3-3.8 center cavity, but the it would add ~R3 to the whole-wall R (as would a non-expanding foam injection into that cavity.)
With both a CMU core fill and 3/4" of rigid foam on the interior you'd be bringing the whole-wall R up to something like R8, (nearly that of a batt-filled studwall) but unlike the typical batted studwall it would nearly air-tight, and the conducted heat loss would be 1/4-1/3 of what it is before treatment. It would be enough to FEEL the difference, and would outperform 2x4 studwall built to "typical" standards as opposed to "best practices, air-tight".