How would you handle a situation if a soldier asked you to just get them barred because they don’t want to be promoted or go to the board?

I will politely disagree with the other posters. I know everyone wants everyone to be gung-ho and push for promotions and performance. But that is not reality. The Army is a pyramid structure. Many lower enlisted Soldiers will do one term of service and then ETS. I am not familiar with the new board requirements, but this is nothing new. The best NCOs should be promoted first and then the vacancies are filled with who is below them. Why would anyone want to force a mediocre Soldier to advance in NCO rank? I don't see how that helps anyone.

You go ahead and bar them. The ALARACT doesn't state they will be barred, only that this is to be considered and SMs should be counseled that if they have no potential for future promotion, they may be barred and separated.
The issue is usually people misreading the message as saying that the SM should or will be barred. That's not the case.

As leaders (NCOs), we should inform out troops about the importance of the board. No one in the Army was ever promoted when the Soldier was ready. If that were the case then no one would ever get promoted. The Army promotes on one's potential to serve at the next higher grade regardless of if the Soldier "feels" ready. You as a leader must make an honest assessment of the Soldier to determine if they possess the potential to serve at the next higher grade.

The reasoning for the new promotion guidance is that Commander's were using the system against the betterment of the Soldier's thus stalling the Soldier's career.

Regardless of whether you agree with the new policy or not, this new system promotes/encourages competitiveness across the NCO Corps. This competitiveness is well overdue, gone are the days of waiting for your handout, I mean promotion.