When aircraft are doing pattern work they are VFR so the separation requirements are 500ft vertical and they need to see and avoid. There is no horizontal spacing requirement.
If tower was online and another pilot is sequenced in front of you by the controller they will need to follow the instruction given so don’t fault the pilot, they’re following the instruction.
If Tower is not online, and the airport is operating without ATC, the same rules still apply with VFR but aircraft will now need to police themselves.
Make sure you are sending traffic advisories on Unicom to the other pilots to let them know where you are in the pattern. Calling inbound once, reporting position when on crosswind, downwind, base, and final.
Mistakes happen though on Unicom, it can be difficult to judge when to slot yourself in without ATC, go around. You have to remain patient.