The Christian Institute is sueing Google on the grounds it is infringing the Equality Act 2006.
The group accused the popular search engine of having a "warped value system" after pointing out that it allows advertisements for "pornography and instruments of violence".
Websites selling knuckle-dusters and ouija boards, as well as dating sites designed for married people who want to have affairs, are advertised on Google.
But the company turned down the non-denominational Christian charity that wanted to pay Google so that whenever the word "abortion" was typed in, its link would appear on the right hand side of the screen.
The link would have read: "UK abortion law news and views on abortion from the Christian Institute."
Google said it had a policy of declining sites which mixed abortion with religious views.
It does, however, accept ads for abortion clinics, secular pro-abortion sites and secularist sites which attack religion.
Entering the word "abortion" into the search area immediately brings the user to adverts for Marie Stopes abortion clinics.
A search of other topics indicates that Google is happy to display ads to its millions of users for many other services.
Typing the words "having an affair" reveals a list of ads aimed at those looking to engage in extramarital relationships.
There are sites advertising advice on outdoor and group sex when words such as "swinging" and "dogging" are typed in.
Google also appears to have few qualms about sites advertising the sale of knuckle-dusters and ouija boards, as well as thousands of ads for pornographic material.
A spokesman for the US company said yesterday: "Google policy does not permit the advertisement of websites that contain abortion and religion-related content. We only allow ads that have factual information about abortion.
"We recognise that this is a very emotive subject and that people have strong views on both sides. Google takes no view on this issue one way or the other as a company."
The spokesman added ads for most weapons were not allowed and those for pornography were strictly monitored. Anti-abortion ads with no religious content would be permitted.
Mike Judge, of the Christian Institute, said the policy was anti-freedom of speech.
"It is insulting to say that a Christian perspective on the subject of abortion would not provide factual information. For Google to suggest that a religious belief means your views on abortion are not factual is outrageous and insulting to millions of religious people," he said.
"The real test of freedom of speech is whether you allow the viewpoint of people you don't agree with to be heard.
"By refusing to allow us to advertise, Google are taking away the opportunity to hear a religious point of view.
"That Google allows ads for all of these other products, including pornography and instruments of violence, shows how warped their value system is."
