I don’t have any firm answers, but I can contribute a key part of the question.
Some people have quoted studies showing that Diet Coke does/does not induce glucose spikes. It’s important to note that most diet sodas switched from aspartame to sucralose recently (in the past year), and the two may have different insulin responses.
If the argument is diet = aspartame = insulin = sugar = yeast, then the major problems with the argument are going to be:
(a) “diet = aspartame”. Diet sodas (since 2005) are predominantly sweetened with sucralose. But most studies will be published before 2005, so the results then aren’t very applicable to reality now.
(b) “aspartame/sucralose = insulin”. I’m pretty sure both sweeteners are in such low concentrations that any insulin response would be minimal.
© “sugar = yeast”. I’m extremely skeptical that body insulin/sugar levels (topologically in the interior of the body) will affect yeast infections (topologically in the exterior of the body).