Is it possible to by-pass restrictions in Israeli adoption law preventing a partner of the biological parent from adopting his/her minor, if they are of a different religion?

Yes! By way of a special judicial “parental order” given by the family court, as happened in November 2015, when Tel Aviv family court granted such an order in relation to two Lesbian women, one Christian and one Jewish, bypassing the prohibition on adoption, in this case. The decision was given in the spirit of precedent set by the Supreme Court in 2014 which eased the recognition of non-biological parenthood.