A poll of more than 600 students and graduates by Milkround.com found 58% want graduate employers to scrap this minimum requirement where it is used.
They want recruiters to understand job suitability cannot be judged solely on degree classification.
Many graduate employers use a 2.1 degree as a benchmark for their recruitment: unless candidates have or are expecting a 2.1 degree they won't even be considered for a role even if they have desirable skills such as relevant experience.
When submitting applications online, 2.2 and third-class degree graduates will often be rejected after an initial batch of screening questions, preventing them from giving evidence of their potential employability beyond academic achievement.
Eva Malecki, graduate recruitment manager at Centrica, said: "We do not have a 2:1 cut-off as we believe that accepting applications from graduates with a 2:2 or above will enable us to attract and assess a larger, more diverse graduate pool, especially as the value of a degree classification can vary from one institution to another. To secure the best talent for our business, we look beyond a degree classification; job history, activities and interests outside of university and competency-based examples are just as important to show us an applicant has skills beyond their degree."
However, among the 42% who think the 2.1 minimum requirement should not be scrapped, one respondent said: "If the minimum requirement is scrapped, students won't try so hard and will become lazy knowing that getting a graduate job won't be as competitive. This is a waste of taxpayers' money and a decision that would punish those who work hard to achieve success."
Milkround.com spokesman Mike Barnard said: "Graduates who don't have a 2.1 degree will always be frustrated by its appearance as a minimum requirement, but recruiters are facing far more applications than ever before as the demand for jobs is high: a 2.1 minimum is a simple way to cut applications down, save time and get a highly academic candidate.
"However, any recruiter who enforces their 2.1 minimum risks missing out on non-academic talents that could be vital to a role but not associated with the level it says they achieved on their degree certificate. No institution is the same so it's also important recruiters understand a 2.1 degree from one university may not be comparable to a 2.1 degree from another."