You control scope, cost, schedule; everything you do responds to those numbers.
First, I'd make sure that my team and if possibly my customer have received the requisite training (that's a joke - go view the video, you'll thank me).
Then I just add the clients' requirements to the requirements, project the impact on cost, scope, schedule, and quality and let the client make an informed decision.
me:"we want to use the term accepted by the industry" boss:"well that's unacceptable - I think the term is outdated - find another"
OK, We'll check on that and see which way the industry is evolving. I'll just insert a new workpackage here that will delay your schedule by between 1 and 4 weeks - we'll project 1, and that will increase the cost by $X. Of course if you are right and the term is outdated, it will also increase the costs in other ways - as I said, the industry uses this term, and resumes, capability statements, etc. will be phrased in terms of industry best practice. I'll work up a better cost estimate after the research, but I'd estimate it will increase the total cost project by 10%.
me:"the solution has to be routed through authentication services to ensure they are a member of your staff and to identify who is using the system like you want" client:"well that is unacceptable - they shouldn't need to authenticate"
Understood; we can do the project without authentication. Let me draw your attention to the tension between that new requirement and your earlier non-functional requirement on security. The only way to reconcile those two requirements is to implement some pretty cutting edge technology that I would recommendcan't guarantee is reliable, nor can I guarantee that you carefully consult withthe user experience will match your General Counsel aboutrequirements in that area.
I'm not comfortable with this new requirement, so we're going to re-assess the impact on the project and let you know of any legal liabilitychanges in cost/scope/schedule. If you'd like we'll We're also research the likely costsgoing to do a quick risk assessment (at our own cost), and other penalties resulting from hackers using this system as a launching pointpart of the project acceptance test/closeout, we'll ask for spam and other attacks. We'll be updatinga letter from your general counsel stating that we did the project according to your requirements and scope of work to show that you requested there be no authentication so that we'll be clear ofwe are indemnified from any legal or, ethical liabilityor other consequences.