That's highly debatable. Also, obviously 'most' begs the question 'most by what?' if it's just by number, then that seems unlikely but possible. But most by weight, volume, or, more importantly, functionality - not really, that's definitely human cells.
Interestingly, you're right in that the "most of your cells are bacteria" point is a myth. I'm not a specialist, and fell for the pop-sci BS. Apparently the real ratio is closer to 1:1 ( https://www.nature.com/news/scientists-bust-myth-that-our-bo... ), if we can trust Nature's summary of several recent articles.
With regard to functionality, that's a very open question. We're constantly finding that features that didn't seem useful are not just functional but important. This trend can be seen at multiple levels, from gut flora to "junk DNA."
As for what fraction of our genome is either shared with other non-human organisms or originated with them, it's tough to find a straight answer on that, but rest assured it's far from zero. See https://www.cshl.edu/the-non-human-living-inside-of-you/ . That's been well-understood by everyone other than religious fundamentalists for some time now, and there are countless legitimate sources that can be cited.
I am no religious fundemantalist (I'm actually an atheist), and care very little for the notion of purity of humanity. The idea of 'human DNA' vs 'non-human DNA' seems suspect to me, as in some trivial sense, anything that is in the genome of a human being is by definition human DNA, and on the other hand, you can find large swaths of human DNA that are identical to most mammals, and probably a few that are common to virtually all eukaryotes. I also know that viruses can leave long-lasting changes to your DNA, that may even be heritable I think.
Still, related to the importance of bacteria, while I don't doubt that, as we learn more, we will discover that they have a bigger role than even dreamed 50 years ago, you still can't compare it to the basic roles of human organs. We have actually created microorganism-free mice and other organisms, and while they are not very healthy, they are fully functional (with bad digestion and big immune problems): https://en.m.wikipedia.org/wiki/Germ-free_animal
