The Facebook group at the centre of these efforts, Mary Should've Aborted, was created in February and has more than 3,000 likes.
"America Needs Fatima," a website started by the conservative Catholic group American TFP, has a petition calling for the group's removal.
As of Thursday, the petition calling for the group's removal has more than 15,000 signatures, or roughly five times the number of likes Mary Should've Aborted has.
"This page quite obviously violates Facebook's hate speech policies. And it is offensive to the belief of over a billion Christians worldwide and directly offends, insults, demeans, and shows hatred for what Catholics hold most dear," reads the petition in part.
"Many of the comments, especially those of the page's creator, clearly show the intent is to vent hate and insult the Catholic faith. Facebook should not be a platform for bigotry against Catholics."
On the petition page, America Needs Fatima also provided directions for how to report the page on Facebook as well as other offline contact information for the Facebook company.
On Wednesday, the Facebook group "Catholics & Protestants Against FB Religious Discrimination" was launched and gained about 200 members in a day.
"Facebook allows Atheists to have BLATANTLY offensive pages against Christians. We exist to remind Mark Zuckerberg and FB to follow their own policies," reads the group's description.
Cary Bogue, spokesman for the group Catholics & Protestants Against FB Religious Discrimination, told The Christian Post that this went beyond ideological disagreement.
"We're not trying to censor anyone, but this falls under the category of hate speech," said Bogue, who added that this was the first Facebook group his page had gone after.
"It's one thing to say we're atheists and we're proud of it…it's another thing to say his mother should have aborted him."
The main page for Mary Should've Aborted includes a cover photo showing the Virgin Mary smoking a joint with the quote "she is higher than all Catholic priests, even higher than the twelve apostles. In fact, she is higher than every single angel."
According to its description the group has two admins, a pair of 20-something students doting the names "Z" and "Lilith." They state that they are concealing their true identities to protect themselves from bodily harm.
"The bible is a load of out-dated traditional horse manure and has no place in education, laws, politics or government," reads the description in part.
"Organized religion is a man-made tool to control society and justify oppression, currently dividing and destroying the planet."
The group's description states that they "highly encourage" debate on their postings, with those offended being their "target demographic."
"I do not seek to convert people, other people's beliefs do not bother me until they deny others rights and happiness," reads the description.
According to Facebook's guidelines, while the social networking site "distinguishes between serious and humorous speech" hate speech is not permitted.
"While we encourage you to challenge ideas, institutions, events, and practices, we do not permit individuals or groups to attack others based on their race, ethnicity, national origin, religion, sex, gender, sexual orientation, disability or medical condition," reads Facebook's guideline.