Holy Church teaches us that we are to avoid both near occasions of sin AND the possibility of causing scandal.
You would not Cross yourself upon entering a Prot building because the Real Presence is not there. Ditto for a former Church that is now occupied by heretics. Therefore, you shouldn't go into such a place because exposing yourself to their errors opens up the possibility of being deceived. Never forget that the Devil is after your soul.
Further, someone could see you entering such a place and could assume that you agree with the teachings of Newchurch and/or that they themselves should go in and 'fellowship' with heretics. We must guard against the chance that our unspoken example might lead others to sin.
Believe me, I understand your frustration. My maternal grandmother (who lived and died a traditional Catholic) was a parishioner at one of the most beautiful churches I have personally ever seen. I LOVE the artwork, the statuary and the High Altar, which still stands entirely intact behind the Newchurch picnic table. The tabernacle is still in the center of the Altar, the candle-stands are still in use... simply a gorgeous place.
It breaks my heart to know that a false Prot-Masonic/Jєω-heretic service is offered where the Holy Sacrifice used to ascend to God for the salvation of souls. That means I have to avoid a place not only full of fond personal memories, but a place designed for God's glory that has been hijacked by His sworn enemies.
St. Anthony of Padua, hammer of heretics, terror of Hell, pray for us.
Our Lady of Ostrabrama, pray for us.
Most Sacred Heart of Jesus, have mercy on us.