I think with this path access=private might be more appropriate (with the same tag on the gate nodes), assuming that you have to be a member/allotment holder to gain access.

The access=customers tag tends to be used more where a customer can just turn up, e.g. retail parks and their car parks.

There's no need to change it if you're happy with the current value. That should still stop routing software from trying to use it as a through route, although it may be a couple of weeks before it takes effect.