The employees are in a different situation than you, as a partner. The employees can be forced to sign under threat of termination. There is nothing preventing them from being fired for not signing the agreement.
That said, under Minnesota law, an non-compete agreement is not enforceable unless it is supported by independent consideration. That is just a way of saying, unless he pays them something or gives them something of value, it won't be enforceable. Continued employment is not "independent consideration" since they already had that before the agreement.
As for you, as a partner, you certainly don't have to sign something you don't want to. It would depend upon your partnership agreement, but you already have an obligation to the partnership anyway. There would be no recourse against a partner, other than threatening to dissolve the partnership, which again would be governed by the partnership agreement.
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