You have both a political problem and a process problem. There is no silver bullet, and you can't fix these problems solely within the team. Instead, you must rely on the agile concepts of transparency and visibility to ensure that the costs associated with bypassing the process are charged to the project budget.
Make Costs Visible
In agile frameworks, change is never non-negotiable. If you are faced with "non-negotiable" requirements that make the goal or plan for the current iteration obsolete, then the team must scrap the plan.
This is true regardless of the agile framework you're using. In Scrum, the Product Owner cancels the Sprint and the Scrum Team returns to Sprint Planning. In Kanban, work is pulled off the board to meet work-in-progress (WIP) limits, and queued in the appropriate bucket until capacity is once again available. Your specific framework may vary in the way it implements this freeing up of capacity, but it's an essential component of any viable agile (and even non-agile) process.
The cost of replanning and re-queuing is made visible through metrics such as cycle time, cumulative flow, velocity, burn-down, or other framework- and implementation-specific metrics. Communicating about these costs is also essential. By presenting the data to stakeholders and company officers, you place the responsibility for those costs squarely where it belongs.
Schedule risk (like any risk) can be accepted, transferred, or mitigated. Which of these three options is best is a business decision, not a team decision. Regardless of the choice, senior management owns both the choice and the outcome.