The campaigners are angry at plans to transfer more than 1,300 NHS employees into a new subsidiary company.
They argue the move, proposed by Dorset HealthCare, Dorset County Hospital, and University Hospitals Dorset NHS Trusts, goes against ministers' promises to insource public services.
Staff, including porters, cleaners, catering and estates team workers say the move would threaten their pay, pensions and job security, and create a two-tier workforce within the NHS.
Unison South West regional secretary, Kerry Baigent, said: 'Porters, cleaners, caterers and estates staff are the backbone of every hospital. They deserve the same rights and protections as any other NHS worker, not the uncertainty of being outsourced to a private company.'
In response, chief executive of University Hospitals Dorset Siobhan Harrington and chief executive of Dorset County Hospital and Dorset HealthCare Matthew Bryant, said: ‘Staff working in estates, facilities management and procurement are highly-valued colleagues and absolutely central to the provision of safe, effective patient care. We are committed to engaging with them to protect services across Dorset and maintain long-term security for staff.
‘Any new subsidiary company would be 100% owned by Dorset County Hospital, Dorset HealthCare and University Hospitals Dorset. Very importantly, colleagues would retain their NHS terms and conditions, and their NHS pension. Over the last 10 days we have welcomed union representatives to our three public board of directors meetings to ask questions before the subsidiary company proposals were discussed.'