The Christian Institute (CI) accused Holyrood's equalities, human rights and civil justice committee (EHRCJ) of "bias" and inadequate scrutiny.
MSPs on the committee are considering a petition calling for "the provision or promotion of LGBT+ conversion therapy" to be banned.
It defines this as "forced conditioning against a person’s sexuality or gender identity".
The CI, which was part of a coalition that successfully challenged the Scottish Government’s Named Person scheme in 2016, raised concerns that seven out of ten committee members, including substitutes, have publicly backed the campaign.
In a letter to Holyrood’s Presiding Officer Alison Johnstone, the institute said: “This means that many of the committee members have felt obliged to publicly declare their prior support for the terms of the petition every time the committee meets to scrutinise it.
“How can the committee be expected to exercise impartial, critical judgement when most of its members have given assurances directly to the campaign group whose claims they are scrutinising and have promised to enact the very policies being sought?”
Scottish ministers have already announced their intention to ban conversion therapy.
However, CI said there was no agreed definition of the practice.
Its deputy director Simon Calvert said: "Ill-thought-out conversion therapy bans in other countries are being strongly resisted by churches, not because they wish to practise ‘conversion therapy’, but because the bans go much further and outlaw innocent, everyday church activities, including people praying for their friends.
"It is very regrettable that concerns such as these seem to have fallen on deaf ears with the EHRCJ.
"The public expects impartial scrutiny. Instead, committee members have made promises to campaign groups and taken evidence disproportionately from those supporting the petition.
"The Christian Institute was involved in the successful legal challenge to the Named Person legislation where Parliament failed to properly scrutinise proposals.
"Inadequate scrutiny by Parliament in this case may again result in human rights challenges being brought against any resulting legislation."
A Scottish Parliament spokesman said: “Any correspondence received by the Presiding Officer will be given proper consideration and responded to accordingly.”