Farmers say they have sympathy for a "sacred" bullock facing slaughter, but still feel the animal must be put down.
Monks at the Skanda Vale Temple in Carmarthenshire are campaigning to save Shambo, a six-year-old British Friesian which tested positive for TB.
The National Farmers' Union (NFU) Cymru said exceptions could not be made.
Meanwhile, a prominent member of the Hindu community has warned that the wrangle was "making a mockery of Hinduism" and ignoring health issues.
Skanda Vale Temple, known as the Community of the Many Names of God, is a multi-denominational monastic centre at Llanpumsaint, which embraces all religious faiths and includes three Hindu shrines.
A notice of the intended slaughter of Shambo has been issued, and the bullock is due to be killed by Monday, 21 May, according to Welsh Assembly Government rules.
The Skanda Vale monks have said they will create a human chain around the bullock to prevent the slaughter.
Shambo's plight has also attracted parliamentary support - with one MP tabling a Commons motion asking for the UK Government to grant the bullock a reprieve - and has generated interest online.
Following an online petition with more than 6,000 names, the monks are trying to set up a webcam - dubbed Moo Tube - so that supporters around the world can keep an eye on Shambo.
But despite the global attention created by the monks' campaign, the final decision on Shambo's fate rests with the assembly government.
Government vet Christianne Glossop has visited the temple
NFU Cymru president Dai Davies, who is a dairy farmer in nearby Whitland, said the case was "a difficult one".
"There is always sympathy to anyone who has livestock slaughtered," he said.
"But it is a crippling disease and the only strategy from the assembly government at the moment is the slaughter of infected cattle.
'Find a solution'
"If you have an infected animal, it's a reservoir of infection."
The temple's Brother Michael claimed that the case could become an international incident, and said the assembly government had the flexibility in law to make an exception to save Shambo.
"We have appealed for them to use that discretion. We hope we can work together to find a solution that doesn't involve killing," he said.
However, Jay Lakhani, director of the Vivekananda Centre, a London-based Hindu cultural organisation and director of education at the national temple body Hindu Council UK (HCUK), urged Hindus not to blow the issue out of proportion.
He warned the wrangle over Shambo was "making a mockery of Hinduism" and also ignored the serious health issues at stake.
Mr Lakhani said the Hindu religion placed a "great deal" of emphasis on the importance of using "rational faculties" when deciding on religious issues.
He said: "If there is even the slightest risk of the disease spreading to other animals or even humans, then the way forward would be to put down the animal.
"The life of the bull is sacred but so are the lives of other livestock or humans who may - even accidentally - come in contact with this bull."
But other members of HCUK have called for the bullock - which has lived in isolation since testing positive for bovine TB - to be spared.
An assembly government spokesman said: "Wales, in common with many other countries, implements a control policy, based on testing and the slaughter of animals believed to be infected, in order to protect both human and animal health.
"We fully understand that this can be distressing for the owners, but these measures are in place to protect public health and animal health and prevent the further spread of the disease."
Last year, 5,220 cattle in Wales were culled because they failed the TB test.