The riders don't get to choose.
The leader of a classification in a stage race must wear the jersey of the classification that they are leading. In instances where one rider is leading multiple classifications, the UCI sets the general regulation for precedence of the leaders' jerseys. Per §2.6.018 of the UCI Road Race Regulations,
If a rider is leading more than one classification, the order of
priority of the distinctive jerseys shall be as follows:
- general classification by time;
- general classification by points;
- general climber's classification;
- others (young rider, combined, etc.); the order of priority among these other jerseys shall be set by the organiser
In this situation, the organiser may require another rider next on the relevant
classification to wear a jersey which is not being worn by the leader of that classification.
However, if this rider must wear his world or national champion's jersey, or the leader's jersey of a UCI cup, circuit, series or classification, he shall wear that jersey.
The classification leader's jersey supersedes any "special" jersey the rider would otherwise be wearing; for instance, if the current world champion is leading the general classification by time of a stage race (yellow jersey), they would wear the yellow jersey for as long as they were leading that classification. As noted above, this does not apply to those who are the "runner up" to a rider who is leading multiple classifications.
With that in mind, the full hierarchy for jerseys in a stage race is:
- GC (by time) leader
- GC (by points) leader
- Climber's classification leader
- Additional stage race leader's jersey (if applicable; race organizer's prerogative)
- Series leader's jersey (ie, Women's World Tour leader's jersey)
- World champion's jersey
- Regional champion's jersey (ie, European Champion's jersey)
- National champion's jersey
- Stage race classification "on loan" from the actual leader
For instance, in the last stage of the 2022 Tour de France, Jonas Vingegaard was leading the general classification by time (yellow jersey) and the general climber's classification (polka dot jersey). The yellow jersey takes precedence, so he was wearing the yellow jersey. Simon Geschke was in second place in the climber's competition, so he wore the polka dot jersey ("on loan" from Vingegaard).
However, if, in that example, Geschke happened to be the German Road Race National Champion, then he would've worn his German National Champion jersey for the final stage, instead of the climber's jersey. In that case, it's likely up to the organizer (ASO) as to whether the third place rider (Giulio Ciccone in this case) would wear the climber's jersey.