Here is the scenario:

In "Dark Pursuits" Chapter II (pg 431) under 341 Beta-Sky the book states that a Difficult -10 Tech-use test is required to commune with the shuttle's machine spirit and convince it to reveal its secrets. Well none of my PCs are Adeptus Mechanicus, but some do have Tech-use known or +10. Performing any rites to commune, appease, or praise the machine spirits are reserved for members of the Adeptus Mechanicus or allied groups (Tech Marines).

My question is, can my non-mechanicus PCs attempt to interact and retrieve info from a cogitator or Ships data systems? and if so, does it maintain the Difficult -10 penalty for Tech-use as stated in the book? Also, how would you guys/girls explain this concept to players that are new-ish to 40K?

That's just flavor text to remind us how silly the whole mechanicus tech-rites thing is. Anyone who uses technology on a daily basis will know how it works. The 'rites' are simply pressing the proper buttons in the proper order, which anyone with keyboard training will be able to do.

It's a -10 tech use test to do the thing. Background is irrelevant.

For new players, the whole Mechanicus religion thing is a joke about dancing pigeons .

Since the technical part is answered, led me add the following

Performing any rites to commune, appease, or praise the machine spirits are reserved for members of the Adeptus Mechanicus or allied groups (Tech Marines). (...)

In my opinion, you are wrong about that. It is a tat more complicated, but, in turns, makes things a lot easier in the game.

It is only allowed to commune, appease, or praise the machine spirits in the proper ways. Doing it any other way is Tech-Heresy.

So, what are the proper ways ? Good that you ask! Because "you" don´t know. The Mechanicus does, so. And they only telll it to those that adhere to their Cult. The more you adhere, the more likely you are to get told. In fact, the Mechanicus is a good example of a mystery cult: they know something important, let you know that they know but in turn tell you that it is a secret they will keep "among their own". To know the secret, you need to join and strive within their ranks. By joining, you play by their rules and allow them to dictate you what you are to do and who you are to tell.

Also, how would you guys/girls explain this concept to players that are new-ish to 40K?

I explain it as similiar to (primitive) animistic/shamanistic religious believes. Most roleplayers have an idea about how druids/tribesmen thank the tree for the leave they have cut (with a quick "thank you") or honour the dear they killed with sing-song praise while they gut it. It is the same with the use of the machine.

A note on the side: on this basis, I guess a feral world character could have an actual rather easy time "understanding" technology the way the Imperium "understands" it...it might sound oh so familiar...no matter how strange the items and their powers actually are.

[EDIT: improved my gramma]

It is not so easy to state that anyone knows how things work, but there are a myriad of simple rites that are commonly known, as they are vital to operate machinery in the proper way. The Cult has not enough members to operate all machines themselves, so simple rotes are given to the lay operators. The populace of the Imperium has no reason to doubt the truth of the Cult Mechanicus, as the rites provided work .

These can even be used as a connection to the real world:
You may not know the history and original meaning of the symbol (I) on the front of your home cogitator, but you know it is the first step in the Rite of Booting . The next step is the pressing of the symbols CTRL, ALT and DELETE, another ritual that has little deeper meaning to the common citizen, yet still performs its intended duty.

I will actually go far enough to theorize that even it the real world, the majority of users of various technologies has no deeper understanding of the mechanics and science involved than pragmatically how it operates and a limited arsenal of explaining words such as electricity , microwaves and processors. Let us not forget that we live in a highly educated time and place, and that our biases and worldviews are not necessarily valid everywhere, especially in fictional universes.

EDIT: For an excellent treatise on the nature of the Machine Cult, see https://community.fantasyflightgames.com/index.php?/topic/127196-modifying-weapons/?p=1338222