If it's happening locally (likely) and if it's handling certificate validation correctly (way less likely), then there's no difference connection-security-wise

If it's happening locally (likely) and if it's handling certificate validation correctly (way less likely), then there's no difference connection-security-wise between the AV tool running or not running. Of course, AV tool will still mess with your connections and break them in interesting ways, but that has been true since the beginning of AV and in case of local AV you can at least ask to user to try and turn it off. If it works then, you can blame the AV software. If you have a proxy server which does, for example, duplicate some POST requests, accountability is much harder und you will probably have to resort to adding workarounds for the issue (this has happened to me).