The campaigners are also concerned about the potential impact on the environment.
“The data centre planned would be an environmental nightmare both for the wildlife and the local residents,” said Lizzie Bailey, who lives locally.
“This will be temporary disruption with the construction but then permanent disruption because of the diesel generators, the noises, the cooling fans, things like that.”
Curtis Hall Ltd, the company behind the plans, said the development would “not put a strain on the energy grid or water infrastructure”.
The company added: “The data centre’s water and drainage requirements have been developed in consultation with Welsh Water and any connection to the public network requires their agreement.
“This ensures our data centre can be accommodated without impacting the supply of water to residents’ homes.”
It said a “detailed noise impact assessment” concluded the site “won’t have adverse impact on the nearest homes in terms of noise, including at night”.
Cardiff Council said the proposal was being considered, adding that “as with all planning applications, the proposal will be assessed against relevant planning policies and material planning considerations”.
The council encouraged people with “comments, concerns or views” to submit them through the consultation process.