In world orthodoxy, it appears to be quite common for mission parishes to rent part of a Catholic or Protestant church or to share a chapel. For example, for a while, the Kona Hawaii OCA mission used a small historic Catholic Church for their services as that church was only used one Sunday a month by the Catholics. The priest would load all the icons and sacred items necessary for the Divine Liturgy in his car, transport them to the Catholic Church, set up the church for the Divine Liturgy, take it all down once the service was over, and then cart it all home.
I have never observed this sharing of facilities with Catholics/Protestants in the GOC as most missions are either started in a home, a rented and dedicated facility, or a chapel or church that they have built or purchased.