Currently, an adult who has been diagnosed with gender dysphoria and lived for two years as a person of the opposite sex can apply for a gender recognition certificate, before being issued with a new birth certificate.
Fewer than 5,000 have been granted since the 2004 legislation came into force.
Jeremy Corbyn criticised the current law that forces transsexuals to discuss their condition with a doctor before their birth certificates can be reissued declaring that they were born in their chosen gender.
Corbyn said it was wrong the law "forces them to undergo invasive medical tests".
A spokesman for The Christian Institute said the comments were disappointing.
He said: "Gender dysphoria is a psychological condition. People who believe they are trapped in the wrong body need patient help to come to terms with reality."
Simon Calvert, deputy director of The Christian Institute had previously written about the issue and said while transsexuals are entitled to the same dignity as anyone else, politicians must not force people to agree with transsexualism itself.
He called the MPs report calling for a move towards "self-declaration" of gender, an 'X' option for passports and 16 and 17 year olds to be allowed to apply for gender recognition as "morally and scientifically illiterate".
Calvert added: "Transsexual people need patient help to come to terms with reality. The law must stop forcing people to lie about other people's gender."
The Labour leader called on the Government to "update" the current law at an LGBT event which also saw the Education Secretary disparage people who hold traditional views on sexuality.
Justine Greening said there were merely "pockets" of people who do not support the current LGBT agenda - and they should be opposed by the Government.
