Flight Instructor with student reported aborting the takeoff when they received a call from another aircraft warning of an aircraft on the runway.

Narrative

Winds were shifting between VAR@4; Calm; and 160@4 kts. We (Aircraft X); started up and got the weather - winds 160@4. My student determined that we would use Runway 17. However; Aircraft Z that started up next to us declared that they were going to taxi to depart 35; and listening to traffic calls made it clear that this was the runway in use. As such; I instructed my student to take us to the runup area for 35 instead. During our run-up there was a discussion over the radios to switch to 17; but since the winds had returned to calm traffic calls indicated that Runway 35 was still in use. This was further reinforced by Aircraft A landing 35 as we taxied to hold short; and another aircraft Aircraft B calling left base 35. We called 'holding short Runway 35 on alpha 1' over the radio at this time. Halfway through the base; Aircraft B made a call that they wanted to swap to 17; and would continue onto a crosswind. Since winds were calm according to the windsock; and VAR@4 according to the radio I asked Aircraft B if we could depart 35 - and worked out a plan for us to turn an earlier crosswind to depart before they landed.At this point both my student and I checked the runway; final; and departure leg visually and on ADSB-in before making a radio call that we were departing.About 1;000 feet down the runway Aircraft B called out 'ABORT Traffic entering 17 ABORT TAKEOFF; there is traffic on the runway'. Assuming this was for us I took controls from my student aborting our takeoff and exiting the runway on B1. We taxied back to the ramp; and shutdown. Upon speaking with the pilots of Aircraft B it became apparent that another aircraft (Aircraft Y) had entered Runway 17 while we (Aircraft X) were on the takeoff roll for the opposite runway (35). I went to go found the pilots of Aircraft Y when they returned. They claimed they didn't hear any of our (Aircraft X) radio calls; didn't see us on the runway; and didn't see our ADSB either. We confirmed with other pilots in the air that we did make legible radio calls; and out ADSB-out was working as intended. To prevent this situation in the future I highly recommend that a Tower is installed at LGU; as there is not much more I can do as a pilot. When I clear the runway; have ADSB-out; make multiple radio calls; and coordinate with flying traffic I am doing a lot to ensure safe operation for both my own aircraft; and other aircraft in the area.