I always flush with the lid down. Keeps less in the air.
If you don’t shut the lid before you flush it sends poopoo peee particles flying around the bathroom onto your toothbrush
Mythbusters found it makes virtually no difference, and lid down can actually make particles go further due to the pressure forcing them through a smaller gap.
Myth Busters are not a solid scientific source. I discussed the issue a bit, linking to some papers in another comment here: https://feddit.de/comment/5298414
Although Mythbusters is not a peer reviewed scientific source, they do employ reasonable standards of experimentation.
And the first source you posted is particularly interesting, with similar conclusions to what I remember from Mythbusters; that lids reduce the total number of particles found, but that the particles produced from lid use last longer and are larger. So a lid closed situation can;t really be said to be more hygienic.
Unfortunately on a cursory skimming of the other articles none of them seem compare toilets with lid down to lid up, they all seem to look at lidless toilets only. Thus, they can;t really speak to the topic of lid use being more hygienic without the direct comparison.
