Here's the thing. Experienced employees know that managers value their productivity, among other things. They rarely just arbitrarily insist you do something a less productive way. Most employees value their own productivity above everything else. So for example, let's say one person wants to use a different tool with files in a different format from us all, and is so much more productive with this tool that the time for that employee to convert to everyone else's format when projects are done is much less than the time saved by working with that tool. Sounds great, right?
Until the day that employee is sick or on vacation and stuff happens and no-one can get to their files, or read them or understand them because others don't have the tool or know how to do the conversion. The time lost then is often even more valuable than day to day time, because something has gone wrong and needs to be dealt with immediately.
Or, maybe you're more productive if you work 1am to 9am. But this means if anyone asks you a question, they'll have to wait until the next day to see an answer. This pulls down the productivity of the entire team. Your productivity increase may not be enough to balance this.
Or, maybe you're more productive if you never test anything you write, just toss it to QA to deal with. Never update tickets, just move on without the bureaucracy to deal with. Never fill out a timesheet, attend weekly meetings, provide status updates, help your teammates ... overly selfish focus on your own productivity can be truly awful (I know, I've employed people like that, for a while, anyway.)
A smart answer is aware of this. I might say:
It depends why the manager disagrees. For example, if the manager explains to me that this thing to speed me up a little slows everyone else down, and that on balance the team would be better if I was a little below my absolute optimum, then I would do as my manager asks. Sometimes, managers disagree for other reasons: maybe they don't believe I'll be more productive. In that case I might ask to try it for a short time to demonstrate the improvement. Sometimes it's even just that the manager wouldn't like doing that: in that case I need to explain that I do like it and it makes me more productive. Communicating about the reason for the disagreement is going to be crucial to settling it. And of course, bottom line, it's the manager's team and if there is a process or policy that must be followed, I'll follow it.