You are right. The correct sentence is indeed:

Nous proposons des robes, avec le détail mode qui leur permet de passer les saisons.

Just for extra context, this is a specialized use of “proposer”: in commercial/sales situations, it means “offer X as a product”.

I agree with Jiliagre here, this is just some copywriter who overextended the subjunctive. A factor at play is probably that people tend to associate the subjunctive with an elevated style of speech, which is what one might find in what sounds here like a catalogue or other sales document.