The Equal Opportunities Monitoring Form in your job application asks, under the heading of 'GENDER', "How would you describe your gender identity?" with options...
Sex is the protected characteristic and the only two possible options for sex are 'Female' and 'Male' as defined in the Act and consistent with biology, but you don't ask for that.
'Non-binary' and 'other' are not valid options for sex.
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You then ask "Do you consider yourself to be a trans person?
(Equality organisations use the terms "transgender" and "trans" as inclusive umbrella terms for a diverse range of people who find their gender identity....
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...differs in some way from the gender they were originally assigned at birth.)"
There is a protected characteristic of 'gender reassignment', but the terms and definition you use here are not used or defined in the Act.
Asking about a personal characteristic such as 'gender' that is not a protected characteristic under the Act, may be in breach of the GDPR by processing personal - and potentially Special Category - data without a lawful basis.
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If you choose not to gather data on specific protected characteristics (such as sex), you cannot have the information required to ascertain whether or not you could be discriminating on protected characteristics in recruitment. This could be vital in an employment tribunal.
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If you choose to discriminate on characteristics (such as 'gender') that are not protected characteristics under the Act, you may inadvertently indirectly discriminate on protected grounds.
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Language and meaning of words are important and proper use & understanding of terms is vital so that the public is aware of what rights they have and what your duties are. Any confusion or inconsistency over meaning may prevent people from accessing their rights in law.
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Will you undertake to correct these errors and to review all your other policies, documents, reports, etc to ensure compliance?
Sex is the protected characteristic and the only two possible options for sex are 'Female' and 'Male' as defined in the Act and consistent with biology.
The Equal Opportunities Monitoring section in your job application mentions the protected characteristics under Equality Act 2010 & 'statutory reporting purposes'
However...
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However, you then ask for the 'gender' of the applicant with options:
Male
Female.
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'Gender' is not a protected characteristic under the Equality Act 2010 and is not defined in the Act.
The Diversity details section of your job application has what appears to be a partial list of the protected characteristics under the Equality Act 2010. However, it has 'gender' but not sex.
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'Gender' is not a protected characteristic under the Equality Act 2010 and is not defined in the Act.
Sex is the protected characteristic under the Act, but that is not on your list.