Must be the handshake. Because the tastes in ritual-space design are remarkably similar.

Carrie Tomko, in a comment on the post below, notes the similarity between the modern Catholic liturgists' un-sanctuary and the Masonic altar here.

Note the altar placement in these rooms of the Philadelphia Masonic Temple – quite a remarkable building, really, in an over-the-top rococo-faux-Babylonian sort of way.

Renaissance Hall
Corinthian Hall
Egyptian Hall

Now compare the Gothic Hall of the Pennsylvania Grand Lodge and the Immaculate Conception Catholic Church, of Las Vegas, New Mexico, as renovated by the liturgical-design firm RD Habiger & Associates.

Here are some other entries in the Habiger & Associates portfolio.

Santa Maria de la Vid Priory, Albuquerque, N.M.

Provincial chapel, Adorers of the Precious Blood, Wichita, Kan.

St. Albert the Great Catholic Church, which befitting its Austin, Texas, location, is fronted by a mock oil derrick. (Meantime, the mall-like baptismal pool looks well-suited to the pitching of good-luck pennies, though the purpose of the attached Tiki Hut volcano is unclear.)

St. Francis of Assisi Church, San Antonio. (The field-house effect completed by Jumbotron.)

Completing the Masonic parallel, though not designed by Habiger & Associates, as far as I know, two Italian chapels of the Neocatechumenal Way (which may or may not feature secret handshakes): In Catania, Sicily, and in Florence.