I have a background in mathematical physics and, when I feel like it, I sometimes get involved in engineering projects (not mech-eng though) - not many metaphysically-sympathetic people in those fields, I can tell you :) - so I'm probably eligible to give you an answer :)

I personally don't see problems with what you are having to do. You just have to "reframe" how you are looking at those things.

For example, with those "green" products...

Like you, I think the idea of Global Warming, as promoted by mainstream politicians and their mainstream scientist buddies, is a fear-based scam more to do with the green stuff you keep in your wallet rather than the green stuff than grows on the earth.

But that doesn't mean that I wouldn't like to live in a cleaner, greener environment anyway. I think any product that provides the same level of convenience to our everyday lives but does it in a cleaner way has to be a good thing generally regardless of whether we are being lied to or not.

With regard to the statistics, you can "reframe" it by treating it simply as a learning exercise and set aside the underlying meaning of it.

They might be using accidents as examples, when in reality there's no such thing as an accident thanks to the Law of Attraction, but I think they are ultimately trying to teach you some understanding of the underlying statistical principles rather than being bothered whether you believe in the concept of an accident or not.

I deal with plenty of materially-focused people who would laugh hysterically at the idea that what they have going on in their heads has anything to do with the physical world around them.

That's their choice to believe that way as it is my choice to believe what I want.

I've found that if you don't push your opinions onto other people, they usually don't try to push their opinions back onto you.

With your understandings of these ideas, you can just apply what you know and neutralize any discomfort you might have with "playing along" with the people around you and just let them be as they want to be. It's easier to let people be as they want to be when you are secure in what you believe yourself.

So most of the time, I just lay my metaphysical opinions to one side and just stay focused on the end result, whether that is completing a degree course or engineering project.

With engineers especially, metaphysical and philosophical ideas rarely crop up in any form of conversation so it's pretty easy to keep those opinions to yourself if you want to :)