Is it permissible to work on designing a website that serves as an intermediary guide for booking services between customers and women's hair salons?

There is no objection to designing a website that acts as an intermediary for bookings between clients and female hairdressers for specific services. Not all of their work is forbidden, and the default ruling is that it is permissible to cooperate with them in such matters. If they commit something forbidden, then the sin is upon them, as Allah Almighty says: "And every soul earns not [anything] except for itself, and no bearer of burdens will bear the burden of another."