While there are Internet references to the building's being a museum, those days may be past, as there are "No Trespassing" signs on the front doors and bars on the windows. It could use a little TLC, but it looks to be in decent shape otherwise, and the museum sign is still up front.
A 2017 Texas Historical Marker at the back of Moran Cemetery provides some background:
The Hulltown Church of Christ organized shortly after the establishment of the village of Hulltown (later Moran) in 1883. In the early years, the congregation met in different homes. In 1886, real estate investor, Bem Scott, deeded Block 30, Lots 3 and 4 of the original town site to the church for construction of a church building, and work soon began at the corner of Cooper and Grace Streets. Hulltown/Moran pioneer, John C. English, did the rock work for the foundation while carpenters, E.A. Merritt and Frank McLaury, worked on the building with the help of church members.
Three of the earliest ministers were Silas Scarborough, W.A. Bentley and Squire L. Barker. During his minister, Barker wrote numerous articles for national Christian publications, and while advocating for relief efforts during the severe drought of 1886, he toured Red Cross founder, Clara Barton, around the Hulltown area. The longest-serving minister of the church was Elder, Cole Jackson (1882-1958), who was installed in 1910, a position he held until his retirement in 1949. The property was expanded and remodeled in 1954 with the capacity for almost 200 people.
Although the church continued to prosper, in the 1990s, membership had decreased until the church was closed in 2011. The building was sold in 2016 and a scholarship was created for young ministers at Abilene Christian University with the proceeds. The 130-year-old cast iron bell, manufactured by the C.S. Bell Company of Hillsboro, Ohio, was retained by the membership and relocated to a monument built to honor the church in the Moran Cemetery.
-----
As of this posting, there is no sign of the church bell anywhere in the cemetery, and presumably, it was atop the historical marker's hefty base. Hopefully, vandals have not been at work.