I believe ancestry + familysearch are based on the same dataset - in 1944 the mormons filmed the official transcription of parish regs (done as in absence of civil reg before 1877 it could give some official certification of age when the UK (but not IoM) introduced pensions - also needed post WW1 when the IoM finally gave state pensions). The IGI was based on this filming but later on totally wrecked by the replacement of what appears to have been an excellent transcription by overwiting some entries by 'patron submitted' some of which were pure invention - however this normally adds incorrect data rather than removing entries - my own checking of the 1911 is that it is 99.9% accurate at least for the 18th C tho many registers are damaged and/or unreadable and the igi transcription of 1911 ignored the partial readings present in 1911. I did find a small reg missed by 1911 and this was for 18th C marriages at Douglas St Matthews - these were by special licence only and limited in number.

To return to your problem - can you find them on the 1851 census (or had they emigrated/died by then) - if so what place of birth did they give ? The St Matthew's reg (+ 1911 transcription) also has confirmations - this normally took place at age 16 and was officially needed for marriage tho by early 19th think this was no longer checked - might give a check if the family were actually present on Island in some years - otherwise my best guess is that they were off Island (Liverpool was booming at this time and drew in many Manx for work)