This is about passenger and crew comfort.
Some pilots have expressed concern during the summer that the cabin temperature on the crew boarding is too high, sometimes in the mid to high 30s. The use of the APU to provide cooling air is limited to a short period prior to departure and often the engineers will not have switched the APU on - I'm not entirely sure but it is likely that once the APU is on the engineers must remain on the aircraft in case there is an APU fire. The yellow tubes that provide pre-conditioned air (PCA) will keep an aircraft cool but will not cool a hot aircraft.
There are some things that can be done to prevent the cabin temp from climbing too high on the ground - opening all air cooling vents, turning off the IFE and other non-essentially electrical equipment, turning off some of the recirculation fans and closing the window blinds.
Some captains have been asking crew to do these things after all the pax have disembarked but prior to leaving the aircraft to minimise the discomfort to their colleagues and our passengers for the next flight leg. It is typical of BASSA that they would rather order their members to disobey a legal order of the aircraft commander putting them in a legally difficult position.
This is a safety related issue - you are foolish to board passengers onto an aircraft if the cabin temp is above 30C, BASSA see it as some kind of imposition of a dictatorial management, something to be resisted. It is typical - the answer is no, what is the question. It is classic awkward squad stuff.
Safe working practice trial don't make me laugh, as has been pointed out already, in the sprint to the bunks the crew are quick enough to close the blinds - how unsafe can it be? This is just about being awkward for the sake of being awkward. It may represent secondary IA and put the crews jobs at risk - how stupid can BASSA get?