Sending faxes is a complete waste of time. Offices don't look at faxes, they are normally discarded. Send messages through the Congressional website webforms, those go to the office CRM and are tallied and usually get a response.
It's free and provides tangible/tactile evidence of opposition. I'm faxing my reps now.
Do you have a specific source for this? Or are you just assuming that this is the case based on how most business offices treat unsolicited faxes?