Well ideally I wouldn't want any logging messages to come from Hangfire. Admittedly, our logging solution is a bit overkill. By requirement, we have to interact with a company wide enterprise logger which is a WCF service. But we are working in a Web API solution where we want our own logging. So we are using bits of this enterprise logger to satisfy requirements. Then we have our logging inside our application which is common logging and log4net, and inside our Web API, we are not logging everything.
So even if we change our log4net configuration to say, INFO for example, we would get INFO messages from Hangfire. We are not interested in INFO messages from Hangfire, only things we are explicitly coding for within the application.
Giving users the option to opt in to logging seems like a good approach for those that already having a logging implementation with their application.