I reckon that the tech level and moral standards of the regiment's homeworld may play a big part. Hive worlds can't have widespread contreception otherwise they wouldn'thave such a problem with overpopulation. for the guard, I can see contrceptives in the food for some, some from shrine worlds may take vows of chastity (with punishments for the transgressors) but given the huge size of an armys logistical train (which can only be an order of magnitude biggger in an intersteller war) it woud be easy for any accidents to be absorbed into the campfollowers and non fighting element of the guard who may even have kids of their own.

I think the ecclesiarchy might play a  big part in raising them, and many get shipped out to orphanages from the larger warzones were there is a constant stream of transports (carrying invalids and other individuals back, having dropped off the next wave or their other cargo).in smaller ones, like the Tanith seem to fight in, they are probably not even noticed.

I have actually had this conversation a number of times. The Imperial Guard (most not all) does allow guardsmen and women to have kids. I've read it in the conscript description of the 40k codex, some guard fluff, and its kind of logical with interstellar travel that could take 20 to 40 years, a lot can go wrong. I am shore guardsmen die all the time from accidents as with any machine its nice to have good replacement parts handy. As well as the tabula rasa acter. Starting with a black slate, an impressionable mind ripe for the molding. The makings of a fine soldier if I do say so myself.