Anti-vaccine group CrazyMothers asked that those reporting on their claims stop using the term "anti-vaxxers" because they feel it is "derogatory".
The Facebook-based group tweeted that the phrase 'anti-vaxxer' is "dismissivemy [sic] simplistic, highly offensive and largely false". The group also suggested that the term marginalised women. The tweet asked for "Vaccine Risk Aware" to be used instead of anti-vaxxer.
The group's beliefs hinge on debunked studies linking vaccines to disease and disorders such as autism; a theory peddled by disgraced British doctor Andrew Wakefield, whose work on the subject has been pulled from every journal in which it was originally published.
In response, Twitter users suggested alternative names such as "Plague Enthusiasts".
Another user noted that the term is intended to be derogatory.
Others expressed exceptional anger at the tweet.
A handful supported the request.
The CrazyMothers Facebook-based group alleges links between vaccines and autism, a debunked medical assertion, according to a 10-year population-wide study in Denmark which investigated the purported connection.
Doctors warn that the eradication of many viruses, including measles, requires vaccines, as it is the only form of prevention or treatment.
This comes as regions in the United States are currently undergoing a spike of measles outbreaks, the origins of which are in communities with low vaccination rates.
Measles deaths plummeted after the MMR vaccine was introduced in 1971.