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.
His letter addresses the experiences of MP Dr Lisa Cameron, who represents East Kilbride, Strathaven and Lesmahagow, who said her office had received more than 900 messages, including "abuse" and "cyber bullying" after her stance sparked an angry reaction from some, including SNP members.
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."
An SNP spokesman said: "As the votes last week demonstrate, in common with other parties the SNP operates a policy where votes on such matters are free votes - meaning it is up to the individual MP to decide their vote and that there is no party whip.
"As the Bishop's letter states, Lisa Cameron received such assurances before the vote. That reassurance was also given following the vote. As we have already made clear, no-one would fail candidate assessment because of their religious views."
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