Flight instructor reported multiple instances of near mid-air collisions while operating in the traffic pattern at LVM non-towered airport. Reporter recommended the FAA emphasize adherence to proper traffic pattern procedure especially at non-towered airports.

Narrative

While conducting initial student pilot flight training (including pre-solo students) at LVM; Class E surface area; numerous instances occurred where other aircraft and pilots regardless of type; pilot qualification; local; or cross country violated standard traffic pattern entry and exit procedures at LVM. The often sleepy airport at times has become a free for all where you can get away with whatever you want and as it represents a safe space for doing weird things when compared to nearby BZN which is Tower controlled and suffers from airspace congestion.Since we were operating in accordance with Part 61 & 91 in an airplane not equipped with a two-way radio; my students and I applied strict adherence to traffic pattern entry; exit; and visual scanning techniques before takeoff; while in pattern; and upon landings while taxing. More than once; we would observe Aircraft Y operating opposite direction with us in a non-standard downwind; sometimes below us; sometimes above us; converging; diverging; etc. This would cause us to alter course or altitude in order to avoid an unsafe proximity to the non-standard aircraft.At least a few of these instances resulted in pilots telling us on the ground that they were surprised to see us because you weren't talking on the radio" to which I explained that we have no radio; and that we were flying a standard traffic pattern. After a few of these instances becoming somewhat heated with other pilots stating on the ground that we "had cut them off"; for example; Aircraft Z making a non-standard 5 mile right base at 600 AGL pattern entry to a different runway while we were on final approach to an intersecting runway. We ultimately purchased a battery powered handheld radio with an external antenna while feeling that we had no other choice in preventing a collision. The radio is marginal in its performance capabilities but it does offer some increase in safety.My greatest ongoing concern however is the evident complacency in visual scanning techniques by pilots operating 'ADS-B In' equipped aircraft; plus; a clear disregard for correct pattern entry and exit which more than once put us into multi-wingspan proximity to crossing traffic which was sometimes even overtaking us at a slightly higher altitude while we were climbing in the crosswind turn. My hope is that the FAA can continue to reinforce the threat of automation dependency in midair collision avoidance and reinforce the reality that there are still airspace users without installed electrical systems; 'ADS-B Out'; or even radios. Finally; I have observed just as many instances of non-standard pattern practice by other pilots while operating under Part 135; but in that aircraft there are better radios; and it has been much easier to avoid those pilots who are not playing by the rules."