This is an interesting thread. Valuable advice of learned experts/members is sought.
The following is with limited understanding on the matter.
Private Companies/Firms/Institutions also have to adhere and prescribe to various laws, enactments, rules enforced by Central Govt, State Govt e.g
PF act, Gratuity Act, ESIC Act, SE act, Payment of wages act............etc and have to get the forms prescribed by govt from employees and submit these. If there is a column for religion, it has to be filled. Employment application form may have a column for religion.
It is not drifting from being professional and getting personal and in all probabilities it is not forbidden or prohibited.
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As you are researching the subject kindly share your finding in the forum.
There are some other aspects e.g. if you have to offer prayers on a particular time/day/date as per faith and religion, employer has to take it in account. If one employee mentions that working on Sunday is against his/her religion, he can not be forced to work.
There may be some holidays for believers and followers of a religion which are not national but are valid and are observed by the employees of that religion. If majority of the employees are from particular religion employer may fine tune its policies to suit them,.e.g. dress code and all concerned have to be informed to allow it e.g. Sri Sahib ( Kirpan- a small sword) which a baptized Sikh is expected to always wear, head covering/veil which a muslim lady shall wear, all this is to be informed to security staff and others. An employee on deputation abroad is to be briefed that head coverings are not allowed as per law of the land and employee has to make a choice. Employer may frame some policies and rules so that if employees of one religion are in minority their interest is also taken care of and there is no indiscrimination. No one can be intentionally discriminated against or harassed because of their religious beliefs.
Such indiscrimination at workplace can lead to serious implications. Employers have to subscribe to civil rights and acts. Private Companies/Firms/Institutions might have availed some incentive/relaxation/exemption from govt while setting shop/acquiring land and might have agreed to extend relaxation to individuals from particular ethnicity.