Forgetting to get rid of the kommando's clothes was a big mistake by the nazis. Hence, it is exactly what starts the uprising. Surely the nazis would not have make such a mistake, especially after taking care by themselves of the particularly painful chores of the bodies disposition.
The kommando was already aware of its probable fate so it is intriguing why the director took such an implausible stark to start their rebellion.
You raise a very logical query, however I believe its more from viewing the instance from the "outside" and not from the inside.
If this were a murder/mystery drama your point would be very valid, thats viewing it from the 'outside' as a viewer. The view from the 'inside' had you actually been there in real life, it would have amounted to the following.
The change rooms, gas chambers and crematoria were operating 24/7, sometimes at its peak sometimes not. Many trains/transports containing the impending victims were held up just outside the camp until there was "room to accommodate" them. So you can imagine how frequent and repetitive the work of the sonderkommando was. The nazis never ever "soiled" their hands doing this themselves when theres an army of slaves to do it. So when killing off a previous group of sonderkommando it would not have even occurred to them that by not removing the evidence themselves it could trigger a riot. It was very natural to them that the appropriate sonderkommando would do their regular work and they wouldnt have to get physically involved. Remember there were only x amount of armed nazis at the various stations and they were not that many. They would step in and shoot anyone if they noted any resistance. So its quite logical for them to have left the clothes on the hooks without thinking they were sonderkommando or not.
A flaw in the film I however note is the mixing of the sexes in the change room. This would not have occurred. 'Seleksia' separation on the platform started with all men to one side and all woman, children on the other. As the que progressed to the front (Facing Dr. Mengele) able bodied men were selected for work detail, the rest to the change rooms/gas chambers. Woman occupations for selection were pre-selected as the que progressed to the front. It was important to liquidate the men first for only they can offer resistance especially once realising their woman folk were being murdered off together with their children. Woman holding children would never offer any resistance. The only time the change room/gas chambers were mixed sexes when it was grandmothers, mothers together with their children, boys and girls that were all marked for extermination.
(I have not seen the film yet, so cannot comment on that)
But i can tell you that as a general rule you are right that they were not mixed.
However men and women were put in the same gas chamber and did share the same changing rooms. These changing rooms were massive, in krematoria 2 and 3 they were able to hold over 500 people, who would be herded into the gas chambers, their clothes taken away so that then next group could undress and be forced into the same gas chambers.
Late into 1944 when the wall was built into krematoria 2 to reduce capacity, so that there was not wasted space during executions, a train load of people would be killed together, regardless of any other considerations.
Also ofc, during the liquidation of the family camps at Birkenau, the families undressed together and died together.