In my industry, like many others, COVID vaccines have been mandated as a condition of employment. There has been an exemption noted in many job postings for those with medical or religious objections. However such an exemption must be applied for in advance and would be evaluated by the employer's HR department. Rejection due to discrimination and subsequent denial of future employment would be almost impossible to prove. The (edited for confidentiality) notice follows.
"𝐴𝑙𝑙 ... ℎ𝑖𝑟𝑒𝑠 [𝑖𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔 ...] 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑓𝑢𝑙𝑙𝑦 𝑣𝑎𝑐𝑐𝑖𝑛𝑎𝑡𝑒𝑑 𝑎𝑔𝑎𝑖𝑛𝑠𝑡 𝐶𝑂𝑉𝐼𝐷-19 𝑎𝑠 𝑎 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡, 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑟𝑒𝑎𝑠𝑜𝑛𝑎𝑏𝑙𝑒 𝑎𝑐𝑐𝑜𝑚𝑚𝑜𝑑𝑎𝑡𝑖𝑜𝑛𝑠 𝑓𝑜𝑟 𝑚𝑒𝑑𝑖𝑐𝑎𝑙 𝑎𝑛𝑑 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑢𝑠 𝑒𝑥𝑒𝑚𝑝𝑡𝑖𝑜𝑛𝑠 𝑎𝑠 𝑝𝑟𝑜𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑓𝑒𝑑𝑒𝑟𝑎𝑙, 𝑠𝑡𝑎𝑡𝑒 𝑜𝑟 𝑙𝑜𝑐𝑎𝑙 𝑙𝑎𝑤 (𝑖.𝑒., 𝑑𝑖𝑠𝑎𝑏𝑖𝑙𝑖𝑡𝑦, 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑢𝑠 𝑏𝑒𝑙𝑖𝑒𝑓, 𝑒𝑡𝑐.)."
This parallels the Conscientious Objector Draft Exemption based upon a documented religious belief and affiliation that exists for the armed forces. That was often interpreted by the draft boards in a narrow manner that lead to applications being rejected. The rejection of the request from Alvin York, holder of the Medal of Honor and the most decorated American soldier of WW-I as given in the script of the film "Sergeant York."
"𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑤𝑒 𝑓𝑖𝑛𝑑 𝑡ℎ𝑎𝑡 𝑤𝑒 𝑐𝑎𝑛'𝑡 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟 𝑦𝑜𝑢𝑟 𝑐ℎ𝑢𝑟𝑐ℎ 𝑎 𝑤𝑒𝑙𝑙-𝑟𝑒𝑐𝑜𝑔𝑛𝑖𝑧𝑒𝑑 𝑟𝑒𝑙𝑖𝑔𝑖𝑜𝑢𝑠 𝑠𝑒𝑐𝑡, 𝑜𝑟𝑔𝑎𝑛𝑖𝑧𝑒𝑑 𝑎𝑛𝑑 𝑒𝑥𝑖𝑠𝑡𝑖𝑛𝑔, 𝑀𝑎𝑦 18, 1917. 𝑊𝑒 𝑓𝑖𝑛𝑑 𝑓𝑢𝑟𝑡ℎ𝑒𝑟, 𝑡ℎ𝑎𝑡 𝑖𝑡 ℎ𝑎𝑠 𝑛𝑜 𝑠𝑝𝑒𝑐𝑖𝑎𝑙 𝑐𝑟𝑒𝑒𝑑 𝑒𝑥𝑐𝑒𝑝𝑡 𝑡ℎ𝑒 𝐵𝑖𝑏𝑙𝑒, 𝑤ℎ𝑖𝑐ℎ 𝑐𝑎𝑛 𝑏𝑒 𝑖𝑛𝑡𝑒𝑟𝑝𝑟𝑒𝑡𝑒𝑑 𝑏𝑦 𝑖𝑡𝑠 𝑚𝑒𝑚𝑏𝑒𝑟𝑠 𝑎𝑠 𝑡ℎ𝑒𝑦 𝑐ℎ𝑜𝑜𝑠𝑒. 𝐴𝑛𝑑 𝑓𝑖𝑛𝑎𝑙𝑙𝑦, 𝑡ℎ𝑒𝑟𝑒'𝑠 𝑛𝑜𝑡ℎ𝑖𝑛𝑔 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑟𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑐ℎ𝑢𝑟𝑐ℎ, 𝑒𝑥𝑝𝑟𝑒𝑠𝑠𝑙𝑦 𝑓𝑜𝑟𝑏𝑖𝑑𝑑𝑖𝑛𝑔 𝑖𝑡𝑠 𝑚𝑒𝑚𝑏𝑒𝑟𝑠 𝑡𝑜 𝑝𝑎𝑟𝑡𝑖𝑐𝑖𝑝𝑎𝑡𝑒 𝑖𝑛 𝑤𝑎𝑟. 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒 𝑦𝑜𝑢𝑟 𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑥𝑒𝑚𝑝𝑡𝑖𝑜𝑛 𝑖𝑠 𝑑𝑒𝑛𝑖𝑒𝑑."
We may consider that the draft boards of 104 years ago, like the governing political culture and the leadership of the armed forces, was considerably less hostile to religious or political dissent than that of either the government or of corporate HR departments is today. Biden's proposed mandates for all government employment, including contractors, may strip away even the tissue thin provision for an exemption based on Conscientious Objection.
Government and business today under the influence of a totalitarian ideology claim a power greater than that of an absolute monarch. Elizabeth I of England said. "I have no desire to make windows into men's souls." We have General Milley who would never say as Major Buxton did, "York, as your superior officer, I don't feel called upon to look into your conscience."