Alasdair McCrone, of Mull Theatre, and Gordon McLean, of the arts centre An Tobar, were among three directors of the umbrella body Comar.
It looks after a number of arts organisations on the island.
Comar's board said funding restrictions made it necessary to reduce three posts to one.
It said the three existing directorial posts - in theatre/dance, visual arts/film and music/literature - would be replaced by one artistic director who would lead the entire creative programme
Comar, which was created two years ago, said it hoped to continue to work with both Mr McCrone and McLean.
Equity blames poor business planning and is calling on the board to resign.
A public meeting about the decision is to be held in Tobermory next week.
High-profile Scottish actor Alan Cumming tweeted: "This makes me so sad.  Another example of the accountants take over at the expense of the art. And in Mull too."
Former Scottish culture secretary and SNP MSP for Argyll and Bute, Michael Russell, tweeted: "Making Alasdair & Gordon redundant is an extraordinary wrong-headed decision and must be opposed."

Peter Gillespie, 64, from Hertfordshire, was part of a £4.7m plot to bring two million doses of counterfeit drugs from China to the UK.
He was convicted of conspiring to defraud pharmaceutical wholesalers, pharmacists and members of the public.
He was convicted by a jury at Croydon Crown Court.
By mimicking authentic, properly manufactured and tested medicines, Gillespie illegally infiltrated the regulated system designed to protect the public and pharmaceutical industry, the court heard.
The counterfeit medicines contained only a fraction of the correct dosage.
They included Zyprexa, a medicine to treat schizophrenia and bipolar disorder.
Andrew Marshall, prosecuting, said patients had been put at risk by his fraud.
"This case is considered to represent the most serious breach of the medicine control regime - it's the most serious breach that has happened in the EU," he told jurors.
"It has had far-reaching effects for the pharmaceutical industry, control mechanisms, patients and the confidence of the public."
The case arose from a £750,000 three-and-a-half-year investigation by the Medicines and Healthcare products Regulatory Agency (MHRA).
Mick Deats, head of enforcement, said after the trial that 72,000 packs of counterfeit medicine - with a retail value of £4.7m - penetrated the UK supply chain between December 2006 and May 2007.
Some 25,000 of these packs reached pharmacies and were given to patients.
The MHRA was able to seize 40,000 before they got to pharmacies, and 7,000 were recovered following recalls.
Although the drugs contained just 50% to 80% of the correct ingredients, Mr Deats did not believe they caused any fatalities or adverse reactions.
At Croydon Crown Court, Gillespie, of High Street, Bovingdon, was also found guilty of selling or supplying drugs without a marketing authorisation  between January 2006 and June 2007.
Jurors also found him guilty of a charge of acting as a company director while disqualified.
Mr Deats added the MHRA now hoped to seize anything Gillespie obtained through his scam in a proceeds of crime hearing.
Four other men - his brother Ian, 59, of The Green, Marsh Baldon, Oxfordshire; Richard Kemp, 61, of School Lane, Y Waen, Flint, north Wales; Ian Harding, 58, of Lower Westwood, Bradford-on-Avon, Wiltshire; and James Quinn, 70, of Virginia Park, Virginia Water, Surrey - were acquitted of all charges.
Another person connected to the case had already been convicted in the US.
The actors' union Equity has hit out at the decision to remove two of Mull's best-known creative directors from their posts.
[NEXT_CONCEPT]
A man has been jailed for eight years for his part in what has been described as the most serious fake medicine fraud in the European Union.