I ran into this same problem. Schluter all-set (Schluter's thinset that is rated to go both above and below the orange schluter uncoupling membrane) specifically calls out that it is not rated to go over old vinyl tiles. Instead of taking up the old asbestos tiles I bought some really thin plywood, like <1/4" or so, and cut and screwed it down with about a billion screws. That gave me a very sturdy new subfloor that I installed the uncoupling membrane over.
foodlover516 t1_iu1mzsr wrote
Reply to Advice on Tiling over Vinyl Tiles by RatWithChainsawLegs
I ran into this same problem. Schluter all-set (Schluter's thinset that is rated to go both above and below the orange schluter uncoupling membrane) specifically calls out that it is not rated to go over old vinyl tiles. Instead of taking up the old asbestos tiles I bought some really thin plywood, like <1/4" or so, and cut and screwed it down with about a billion screws. That gave me a very sturdy new subfloor that I installed the uncoupling membrane over.