That's why HTML5 specifies the parser, so that every browser extract the same DOM tree from the same input.
The specification is strict in the sense that any parser has to behave the same while also allowing for human error.
... so that every browser extract the same DOM tree from the same input
That is, every browser whose engine has been updated for HTML5 and which also implements the parser specification correctly and without bugs. Which is most, but not all, of them.
My personal preference is to include the optional closings, because XHTML has been around a lot longer and therefore a larger proportion of browsers have been coded to handle it properly and have had more time to work out bugs.
I do like that HTML5 browsers can work around invalid markup in a well-specified way, which is much better than XHTML browsers just showing an error. It's the best of both worlds, especially when the browser's Developer Tools give you warnings about the invalid markup too so you don't need to use an external validator to find them.
