Perhaps when it comes to conversion they go with Orthodox rabbi and do it kadat vekadin but in the rest of the their life they are not “frum”. You do realize that is very plausible.
It’s not at all plausible. If the parents are not observant, and will therefore not raise the child to be observant, then it is impossible to convert him because it is not in his best interest to be Jewish. (Unless the biological father wishes him to be Jewish, in which case it’s not a matter of zochin.)