I'm seeing 2 test failures with the recent change from #6399; in particular, the change to use the "in body insertion mode" directly, instead of reprocessing with the current insertion mode. In both cases[1][2], we lose out on foster parenting with the switch to using the "in body insertion mode", which causes the <p>baz part to be inserted into the table rather than outside the table. Switching back to previous behavior where reprocessing the token uses the current insertion mode seems to resolve the failures.

[1] https://github.com/html5lib/html5lib-tests/blob/master/tree-construction/tests9.dat#L270
[2] https://github.com/html5lib/html5lib-tests/blob/master/tree-construction/tests10.dat#L236