If an officer joins a lodge, then he knowingly accepts that his military rank gets left outside the door (or at least he should know that). If someone else had a problem with it, it is just that, their problem. It wouldn't have to a fraternal organization, some busybody could claim an officer and an enlisted guy were fraternizing if they happened to belong to the same YMCA or both happened to be invited to the same wedding reception. Common sense would tell you (in a scenario presented earlier) that if two lodge members of different military class needed to discuss lodge business, do it off base and out of uniform. Then, it's nobody's concern.
Of course, I was in the small ship navy, so once we hit blue water, most of the standard military protocol was set aside. Our CO was a commander, but he was still addressed as "Captain." The executive officer was called "XO" then you had "Weps" "Ops" "Cheng" and so forth for the senior officers. Most junior officers were "Mr. So and So," and in the evenings after the end of the workday, it was common for the junior officers to hang out on the fantail shooting the breeze or watch movies with the junior enlisted guys. In retrospect, it was most likely age related, but the junior officers associated with the junior enlisted more than the chiefs did.