It's hard to put in practice but respecting someone and liking someone are totally different. I've faced people who I do not particularly like who I can agree with. On that note, people who I like I've had to disagree with even strongly in certain stances. It's about the principle of the message not necessarily the individual.
Liking someone and agreeing with them are two completely different ideas. Often times, people agree on things without even knowing each other, much less liking each other. I have enemies that I do not like, but we both agree that Brad Pitt is still the sexiest man alive. We can have the same opinions, and that does not mean that I have to like them. People have to understand that they will meet people in life that they absolutely do not like, but they can still agree on certain things, like working together for a common good or to get a job done.
No, you absolutely do NOT have to like someone to agree with them. The idea that you should only agree with those that you like is preposterous, and if people actually followed this belief, we would live in a vastly different society. There have been many absolutely disagreeable and unlikable people who have had great ideas, and vice versa. If we were to only agree with those whom we liked, eventually evil would triumph because in my opinion, man is born with animalistic tendencies and tamed by nature. The reason Adolf Hitler got away with killing so many Jews is because he was agreeable and he was likable, and if not for his agreeable nature, so many people would have stood up to him, and many lives would have been saved.