If you were to follow a particular religion...

[Angrboda]

While one can debate whether the Buddha was agnostic with respect to the doctrines of Karma and Reincarnation…

He made his position on them clear in the Mahacattarisaka sutta and further elucidated in others. His thinking was that such views led one toward ethical behavior, but were ultimately speculative. He did use the principles as teaching tools, leading folks ultimately away from them and toward his own teachings, and most importantly, his practices.

Anatta, well, that is never going to sit well with someone who doesn't want to let go of the notion of a soul.

Um, I don't believe in a soul. So, to use your favorite term, "Straw man!"

And the question is not whether the Buddha himself advocated agnosticism on these questions, I'm told he did, and lacking research on the matter, I'm willing to accept that as true, pending further study. The question is whether any particular Buddhism is defined authoritatively by what we have of the Buddha's exposition. (Ignoring side issues for the moment. In one of the sutras, he is reported to have said it is impossible to identify a Buddha, so he himself may not be a Buddha, by his own reasoning.) Off the top of my head, it would appear that many forms of Mahayana Buddhism differ with specific things Siddhartha said, or is reputed to have said. That doesn't make them something other than Buddhism. Arguing that Buddhism is what we have of what he said is an example of the genetic fallacy.

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I got sidetracked by responding to Taqiyya, and forgot to mention a point that occurred to me after my last post. In some deconversion stories, individuals came to disbelief because of their drive to discover the truth. Their zeal in ferreting out the fact of the matter pushed them out the other side of their faith. Of this, it has been said that they do not choose to disbelieve, their understanding of the evidence and facts made it impossible to continue to believe. Religions in general share this property, that we believe them not because we made an explicit choice so much as it was the only choice the person could have made, given what they believed at the time. If I stopped being a Taoist, it would be because the things I believe to be true are no longer compatible with Taoism. And if I were to come to a new faith, it would be based on my knowledge, understanding and belief at that time. It would not be a choice, like picking out a purse, to match my accessories. If you aren't sufficiently drawn to, say, Theravada Buddhism to be one today, I find it questionable that you would become one. This seems to be a question of "What religion do you find least objectionable?" It would still be somewhat objectionable lacking any relevant change — presuming the change mentioned in the OP did not bring about such change.

I don't know what I'd believe then because I don't know what I'd believe, and that would be what determines my choice.