There's a lot of nonsense written about developing rapport. Most of it suggests that rapport requires conscious effort and is inevitably worth that effort. Like much in the self-development field (and, indeed, in all changework fields) this is true, from a certain point of view.
The point of view is that of a self-aware person working one to one. When you have superb state management and a clear purpose, then developing rapport can be a strategic move that gives you more information about the people you need to convince, play or beat to get what you want. Sociopaths can do rapport because it helps them to get what they want and they are never burdened by their impact on someone else.
As soon as you're working with a conscience, you have to question whether your commitment to your goal will override all other considerations and allow you to manipulate other people through rapport. What's likely to happen is that you are going to be drawn into a genuine connection. And that connection can tap into your own weakness or insecurity and shake your ability to manage your own state and to move the relationship.
Someone speaks up in a meeting. And they are edgy and unhappy. To be in rapport with them is to enter some part of that state. That makes them feel visible, but not happy. In fact, you are probably amplifying the state by entering some part of it yourself. Now you have rapport (which gives you the option to interrupt the pattern) but you've lost rapport with at least some of the rest of the group at the meeting and introduced dissonance. At that point, you have to make a decision about where you want to establish better rapport and where you want to let it go.
How good are your judgments when you are in rapport with a state of being edgy and unhappy? Right. You feel tough and decisive and you may even channel that energy to create focus and movement in the group. What you give up to do it is the ability to manage the first relationship. There's a price for moving out of rapport: the price involves someone recognizing (unconsciously) that you have marked them out and then moved on. You haven't made a friend.
What are the other options? You could stay in rapport, but that would fracture the group and probably compromise your own outcomes in a way that is not acceptable. If you have the presence of mind and an opportunity, you could introduce a pattern interrupt. That creates an opening for movement as long as you can dispel the tension. It's hard to do if you're edgy or anxious (or just in rapport with someone who is). Perhaps you can take the discussion off-line so that you can work within the relationship without affecting the group. Perhaps you can find a leverage point to change state without changing the focus of the meeting.
The hard part of rapport is not creating rapport. It's knowing when creating rapport is the right thing to do: right for you, right for the other person, and right for the context. Once you have rapport, everything you do has impact. Sometimes it is better to refuse to enter the rapport if you're not willing to do what it takes to maintain both the relationship and your outcome.