President of the Bishops' Conference of Scotland, Bishop Hugh Gilbert, wants the First Minister to provide public reassurance that freedom of conscience will be protected in the SNP and wider public life.
She fears being deselected from the party after voting in the House of Commons against lifting the ban on abortion in Northern Ireland, where terminations are currently only allowed if the mother's life is at risk or there is a danger of permanent and serious damage to her mental or physical health.
While the matter was a free vote, enabling individuals to decide in line with their own conscience, Ms Sturgeon made clear if she was in Westminster she would vote in favour of "women's right to choose" and the result was 332 votes for to 99 against.
Dr Cameron, a consultant clinical psychologist whose anti-abortion stance is partially due to having suffered two miscarriages, said since the vote she has been subject to "attacks" including a person threatening to "come over and 'abort me'".
In his letter, Bishop Gilbert writes: "In the days following the vote Dr Cameron has been subject to a significant degree of hostility from many quarters, including ordinary members and officer bearers of the Scottish National Party, some of which she describes as being 'nothing less than vitriolic' in nature.
"She adds that according to local officials it may 'now be incompatible to hold pro-life views and be an SNP MP, candidate, to pass vetting or be elected in any capacity'.
"She further notes that, despite prompting, she has presently received no public reassurance from the leadership of the SNP that this is not, in fact, the case.
"I, therefore, am writing to you as leader of the Scottish National Party to seek such a public reassurance.
"I believe I write on behalf of all who cherish freedom of conscience within the public square and hold in high regard those in public life who remain true to their conscience, even at the expense of personal popularity or political advantage."