Disagreement is not disloyalty but antagonist relationships within a team do not help it.  It is okay to have differing opinions and thoughts about a subject or strategic direction.  Part of the reason that people are hired for their positions is because their experiences, opinions, and thinking and so it is realistic to believe that some of them will be different from your own.  In fact, it is arrogant of your leadership to believe that you have all the right answers and to discount the thinking of others.  If you only surround yourself with people who think like you then you don't really need those others.  We need divergent thinking and differing ideas to challenge our own thinking and perspectives and to elevate it.  But never think for a moment that because someone has a differing opinion that they aren't as committed to the team and the organization as you are.  But if you continue to discount their thinking, you will ultimately drive them away from the team and out of the organization.

It were not best that we should all think alike; it is difference of opinion that makes horse races. Mark Twain

If everyone is thinking alike, then somebody isn’t thinking. George S. Patton

The surest way to corrupt a youth is to instruct him to hold in higher esteem those who think alike than those who think differently. Friedrich Nietzsche

Never push a loyal person to the point where they no longer care.  Anonymous

When we are debating an issue, loyalty means giving me your honest opinion, whether you think I'll like it or not. Disagreement, at this state, stimulates me. But once a decision is made, the debate ends. From that point on, loyalty means executing the decision as if it were your own.  Colin Powell