Reading that petition, the route that they are keen on (right turn-out North and then East of Otley) is designed to replace the current left turn-out LAMIX and DOPEK SIDs. There would still be a need to depart aircraft to the West via a NELSA replacement SID.
Not bad news for the residents of BIW and Menston, certainly, a right turn-out LAMIX/DOPEK would reduce the number of flights over their houses by about a third, but there would still be about two thirds going West.
From an ATC point of view, the right turn-out LAMIX/DOPEK would be a hugely positive development, deconflicting these departures from RWY32 arrivals, which they currently cross over with.