It's a myth that if you disagree you cannot commit to it anymore.
The standing notion is if you disagree, then you will be at a cross with the topic, person or project. In work life, that should not be the case. In fact, it's against the positive work culture which dilutes the work environment.
Hence, it's completely wrong, and here is why.
Disagree on the agreed facts and figures
For any agreement and decision, there need to be criteria set out.
Data never lies. So clearly defined data for the outlined criteria can be a decision-maker on its own. People who don't accept this fact tend to argue more. Ideally, you should have the backbone to accept a fact that is misaligned with you. Accept it in an open mind.
You are still committed to the larger picture. Be professional and move on.
Commit to the facts, not to views.
It's difficult but possible. How? Because you are committed to the facts.
Go deeper into the decision making process. Feel free to challenge the decision, get your asks clarified and commit.
I know. It's not easy. Here are 2x tips to ask yourself -
Tip #1: In 6 months time, will I remember this disagreement? Is that so important? It will NOT be if facts/figures display otherwise. Think.
Tip #2: Handle yourself professionally. I call it "late-night radio" jockey voice. It needs to be calm and composed, but emotionless.
Don't fall into the trap of people with egos, high IQ, higher pay-scale, who might provoke.
If you counter, you may win the battle of ideas, but you’ll lose the war of executing on them. Instead, make "patience" one of your principles.