An assembly is provided for an aircraft propulsion system. The assembly includes an anti-rotation lug, a first mount, a second mount and a fastener. The anti-rotation lug includes a first curb and a second curb. The first mount is abutted against the first curb. The second mount is abutted against the second curb. The fastener connects the first and the second mounts to the anti-rotation lug, which lug is disposed between the first and the second mounts.