It doesn't kill all std that could be transmitted from saliva so in my humble opinion , Listerine is not a protection against std...
But for the ones that are going for that service it is a great link since it does lower the risk for some contamination.
Personally we do provide Listerine to all of our clients at our location , but is is more a matter of good breath for us. It is always pleasant for providers and customers when everyone smells good
Here's a link of many diseases that could be transmitted by kissing :
https://www.youtube.com/watch?v=5ed7ES5LBQk
Here's an other one :
https://www.std-gov.org/blog/can-get-std-kissing/#can-you-get-an-std-from-kissing
Also it is important to remember here that the statistics are not based on providers so as providers we have to take in consideration that we are having way more partners then a regular person so the risks are way up. For the clients too because when you are "sleeping" with someone it is like you slept with all her previous partners in terms of contamination so it is the same for all fluids exchange ( including kissing).. I am sorry I know it is raw to read , but as I was saying in my previous comment , it is a very sensitive topic... I am trying to be gentle and to keep to the facts here so I hope nobody will hate me for that ...
As many people said in this thread , the best is to get tested often and to be confortable with your decision once you get all the informations in your hands..