Having worked in an airport, although not having faced this issue (sadly!) I would guess it would have gone like this.
Asked by check-in agent to put clothes on more appropriate to a charter flight (where there will be many familes).
Refusal
Asked again
Refusal and request supervisor.
Supervisor (rightly) backs up check-in agent.
Refusal
Supervisor suggests that Monarch do have the right to stop anyone flying.
Hissy fit, no request to go to the toilet, or possibly refusal due to having to re-join check-in queue at the back. Strips in the middle of the check in hall.
When return from package holiday, make big fuss in the hope for compensation.
All the time whilst fellow passengers and airport staff look at her thinking "what a muppet."