This paper studies practical consensus problems for continuous-time multiagent systems with heterophilous dynamics. Agents in the network tend to cease communication when they are close enough to each other inspired by the heterophily principle in social and opinion dynamics. We propose two types of state constraints on dynamical agents, in which the hard constraint refers to exogenous restrictions that rule the entire evolution of the agent behavior and the soft constraint turns out to be endogenous and only the ultimate equilibria of the agents are restricted. Sufficient conditions have been established to achieve practical consensus for both types of constrained systems. Numerical simulations show that the practical consensus time grows logarithmically, revealing a rapid convergence with respect to disagreement of initial conditions.