you will be surprised to find out that they would probably have no problems whatsoever. Here in NYC, there are plenty of Chaba-run daycare centers with kids that were adopted and did not go through conversion or if did so, went through Reform one. Plenty of kids are children of same-sex couples and that doesn't seem to be a problem with Chabad people running more than 1 center that I know of. Outside of US, Chabad are even less "strict".
Hamas says Egyptian mediation has restored calm along Israel, Gaza border (Haaretz)
from the article: Iceland Jews are left out in the cold