Of course the teachings must be made to appeal to westerners. This does not mean totally gutting them
People who won’t accept anything spiritual or religious don’t need this practise. In Buddhism we don’t try to convert, for some people it is simply not their time
The illusion of self can be observed directly. Perhaps it's even an inevitable conclusion of sufficiently intense introspection. I'd consider observing this to be a spiritual practice.
The metaphysics of realms of reincarnation, hungry ghosts, etc. is religious thought (and it was the dominant worldview when Siddhartha was born). These are not ideas that I can discover independently through introspection; if I believe them it's because someone told me to.
We might be talking past each other, though: if you're saying that the benefits of meditation are inherently inextricable from a Vedic worldview, I don't agree. But if you are just saying we haven't yet figured out which parts of the religion are actually necessary, then I agree. I personally learned meditation in a fairly Buddhist context, and naturally there are parts that resonate with me and parts that don't.
Actually, he mostly invented them, they aren’t present in Vedic texts afaik. Also, he did perceive it independently: his insight became so great that he could see his past lives, and he taught that we can too if we follow the 8fp
Here's where I think we differ: a lot of people in secular western culture are intensely put off by all the religious stuff that comes with Buddhism. The metaphysics and reincarnation stuff is, in my view, a reflection of the culture that Siddhartha Gautama grew up in and taught in, rather than a necessary part of eliminating suffering. I think that retelling these lessons in a way that's accessible to modern audiences is important. Some people simply will not accept something taught in the form of ancient mysticism. Should those people be denied insight just because they didn't grow up in India during the Iron Age?
I get that Ingram is polarizing. I'll add a link to Mahasi Sayadaw as well, but I just don't think he explains things in a way that's as clear to someone with my cultural background.