The Christian Institute has commended the UK Government for deciding that there will be no fundamental change to the Gender Recognition Act.
Amendments to the law would have allowed people to change their gender on their birth certificates without a medical diagnosis.
However, the Government said on Tuesday that the Gender Recognition Act (GRA) already strikes the right balance in providing "proper checks and balances" while supporting people who want to change their legal sex.
Women and Equalities Minister Liz Truss said that instead of changing the legislation, the process and experience of applying for a gender recognition certificate would be made "kinder and more straightforward".
The Christian Institute has a long track-record of opposing plans to allow people to self-identify their gender.
Simon Calvert, Deputy Director for Public Affairs in the organisations, said: "It [the Government's decision] will do much to help protect people with gender dysphoria from being rushed into life-changing decisions which they may later regret - an increasingly common phenomenon. It will also be a relief to some of the families of people with gender dysphoria as they seek to sensitively support them.
"The Christian Institute opposes the existing GRA in principle. Its fundamental premise is that a man can become a woman and that a woman can become a man. But this is a biological impossibility. The act creates a legal fiction."
Contrary to the Christian Institute's views, Ms Truss wrote: "We want transgender people to be free to live and to prosper in a modern Britain.
"We have looked carefully at the issues raised in the consultation, including potential changes to the Gender Recognition Act 2004.
"It is the Government's view that the balance struck in this legislation is correct, in that there are proper checks and balances in the system and also support for people who want to change their legal sex.
"However, it is also clear that we need to improve the process and experience that transgender people have when applying for a gender recognition certificate, making it kinder and more straightforward.
"Our changes will address the main concerns that trans people themselves tell us they have about it."
She said the process would be moved online, and that the fee would be reduced from £140 to a "nominal amount".
More than 100,000 people responded to the Government's consultation which was launched in July 2018 and closed in October 2018.
Nearly two thirds of the respondents said people should not have to get a doctor's letter saying they have gender dysphoria, while four out of five people said a medical report should not be required.
Calvert said he's glad the GRA treats the change in gender with a degree of seriousness.
"Requirements such as medical evidence and a period living as the opposite sex are very limited safeguards given that the person is making a fundamental change of legal status - one with profound social, moral, physical and psychological consequences.
"These limited safeguards do at least allow for third party assessment of an individual's claim of gender dysphoria in order to sift out obviously fraudulent or frivolous cases."
However, the Equality and Human Rights Commission (EHRC) called the Government's decision a "missed opportunity to simplify the law on gender recognition", while the LGBT Foundation said it was "incredibly disappointed", and Stonewall said the moves were not enough.
Meanwhile, Amnesty International UK, Liberty and Human Rights Watch expressed 'huge disappointment' in a joint statement, adding: "Research has found that medical barriers to gender recognition for trans people are unnecessarily intrusive and can harm their physical and mental health.
"With medical requirements still in place, trans people will continue to be forced through harmful processes to have their gender legally recognised."