Are 'clean clothes' more expensive than the alternative?
Suppose a pair of trousers costs €100. Garment workers as a collective receive 3% of the price you will pay in the shop. In this case the amount is €3. In contrast, the brand profits will likely be around 10-15% for budget brands and a lot more for the more expensive ones, meaning that the brand would pocket about €15.
Now suppose the manufacturer prices the trousers at €103 with the sole aim of paying a higher wage to the workers producing them. The consumer pays 3% more, but workers earn double. Alternatively, the manufacturer could absorb the negligible increase and maintain a price of €100 for the consumer and have a €12 profit instead.
Paying higher wages therefore does not have to influence the price you pay as a customer.
There may be other price increases for sustainable garments, such as higher material costs for organic cotton, responsibly produced man-made fibres or recycled material. Given that the fashion industry is also one of the largest polluters on the planet, and has an enormous climate footprint, that should be a price that should be paid, and not offloaded onto future generations as it is now.