Changes to hospital services which took effect over the weekend were met with a protest by NHS campaigners.
A demonstration was held at Dewsbury hospital on Friday by action groups who claim NHS services in the town are being downgraded to save money.
All births which require a consultant present are now carried out at Pinderfields Hospital in Wakefield under the changes.
Dewsbury now has a midwife-Led birth unit (MLU) for low-risk births.
Poorly children who need hospital admission are also now taken to Pinderfields, along with adults who need emergency surgery.
More planned operations and clinics have been moved to Dewsbury.
NHS bosses have insisted the changes are safe, saying using MLU’s for low-risk births was recommended by the National Institute for Health and Care Excellence.
But fears have been raised that women who have complications during childbirth could be at risk after Dewsbury loses its consultant presence.
Campaigner Wendy Senior, a former NHS worker, said: “I’ve been to see the new birth unit and it is very nice.
“But we are going backwards. Women can go into labour in Dewsbury, but if they have complications they will have to be transferred over to Pinderfields. It’s not safe.”
The campaigners said budget cuts by the government and difficulties recruiting some specialist clinicians were behind the changes.
Mrs Senior said: “Dewsbury is being stripped of its services.”
NHS bosses have said the shake-up, which will also see consultant-led A&E care centralised at Pinderfields next year, is not financially-driven.
But Mid Yorkshire Hospitals Trust is facing a multi-million pound budget deficit.
The trust must make £26m in budget savings this year and is among NHS organisations relying on bailout cash provided by the government.
Mid Yorkshire is among trusts which must meet stringent targets on waiting times and cost savings to get all the extra money.
Rising demand on NHS services has sparked fears that the financial situation could worsen by the end of 2016-17 unless the government releases more funds.