"Use whatever tools will make you the most productive. If they cost a lot of money, just talk to us and explain why the tool is important. If we can afford it, we will. If we can't afford it, we will make the best compromise with other tools we can, and we'll work on affording the better tool. If it involves changing something that is a standard in our company, meaning that many people and established processes would have to change too, we're not going to adopt the change quickly -- but we will listen to evidence about why the change would be cost effective and we will be open with you about considering it."
"Use only the tools that we have decided, as a company, to use. These tools are our technology conventions. Whether you like them or not, they are the tools available to you and you will not be considered to be a 'team player' unless you find a way to get your work done with the tools we give you. If you recommend changes we will view it as a waste of your time to even contemplate tool changes, even if you have evidence of their cost-effectiveness. Changing something that is already a standard within the company is impossible unless the idea originates with senior-level employees; the more you ask about changing established policies, the more you will be viewed as uncooperative."
Which of these attitudes falls more under the banner of "technology agnosticism"? In most bureaucratic settings, the second attitude is trumpeted as a pragmatic, technology-agnostic view point. But really it is an excuse to avoid dealing with the consequences of depriving talented workers of affordable, productivity-enhancing technologies (generally for political reasons, like deflecting blame with standards, and emphatically not in the name of legitimate business concerns).
If anything, it is technology dogmatic.
Meanwhile, the first attitude strives to be actually pragmatic rather than merely paying lip service. If a better tech tool is available and affordable: just use it. If it's not affordable: justify it with numbers and be content to wait until it's affordable. If the scope of the change is massive within the company: expect that you will need to present equally massive evidence that the change is beneficial, but also expect that we will appreciate it when you do present this kind of evidence.
That sounds much more technology agnostic to me -- not to mention less dehumanizing, more pragmatic, and fairer. And you will have the benefit that technology policies will be influenced more by technology experts in an organization than by managers.