How would substances that have anti bacterial characteristics interact with yeast?
Substances that exhibit antimicrobial activity do so because the microbe itself is susceptible to the mechanism of action. For example, some bacteria crosslink their peptidoglycan cell wall with a transpeptidase (aka penicillin-binding proteins), and penicillin antibiotics block this step. Other bacteria don't do this, and so if you use penicillin there will be no effect. 

Likewise, some antimicrobial methods have very broad efficacy against everything, like drugs that inhibit ribosomes, or at the extreme end, bleach. Being said, ginger as in the homebrew link is shown to have a broad action on microbes as denoted in the following article. The question now is does ginger affect yeast? 

Google search "gingerol antifungal" (gingerol is apparently one of the potent effector molecules in ginger) and you get a host of results detailing it's efficacy on C. albicans. This doesn't necessarily mean it has the same efficacy on S. cerevisiae, but it does mean that, and this is just a number out of the literature, but a 10% ginger solution may have deleterious effect on fungal growth.

Outside that, I can't really find anything on the actual antimicrobial mechanism of action for ginger, either, so it's difficult to say other than for some reason, they inhibit microbes. They did show that 6-gingerol induces ROS production in tumor cells, which results in DNA damage, but I'll continue to look for an explanation.

What remains, now, is too broad. The ways that antimicrobials interact with different microorganisms is a lot to consider and I can only be about as broad as I've written above without going into a novel worth of text. Hopefully this was helpful!

You can check out this Sigma page on antibacterial modes of action to get an idea of the ways different antibiotics are made to affect microbes.