The department’s budget has already been cut by £1.8 million in the last two years, and the latest redesign takes account of further cuts of around £1.9m.
This would leave the library service with a budget of £2.2m a year – less than half what it was 2015.
Councillor Kath Pinnock, who represents Cleckheaton, said she feared the town’s library, which was one of the busiest in the district, would be under threat again.
“It’s so short-sighted to reduce the library service further. They should be looking at innovative and imagination ways to move forward.
“I will oppose any proposals to close libraries such as Cleckheaton, which is unacceptable.”
A similar consultation exercise took place ahead of a decision in late 2015 by the authority to close two libraries, withdraw the mobile library service and cut the opening hours of the other 24 libraries.
The cost-cutting plans involved keeping eight full-staffed town libraries, including Cleckheaton, Heckmondwike and Birstall, and 16 community-supported libraries, but saw 88 full-time equivalent positions lost.
Of the latest consultation, Councillor Graham Turner, joint cabinet member for resources, said: “We know that there are many people who are keen to have their say on the subject of libraries. It is very emotive and the service has already changed massively in the last few years.
“The process needs to be as open and transparent as possible. We must engage with communities to deliver our services, working in partnership with community groups. Many of our services are already supported by `friends of’ groups and volunteers and we must continue to grow this model.
“The outcome the Council is seeking is for residents and communities to be able to readily access information and services in order to improve the customer experience and journey, first time, more of the time. It is important that we become less reliant on buildings and think how the service can be best delivered.”
Councillor Musarrat Khan, the joint cabinet member added: “The way people use libraries is changing, and Kirklees Library Service has to modernise to reflect this. There is some great work taking place, with children and young people’s groups in reading and coding clubs, with health and wellbeing activities, and with business events.
“I would like all these groups to take part in the consultation for us to develop the best, most innovative service we can, given the budget we have.”