1. Liberty is based on political difference.
It may sound counterintuitive but we shouldn't want our party to be the only party because the other party (or parties) helps keep us in check and that ultimately helps protect our liberty. This is rooted in our history.
Two parties emerged from the first Constitutional Convention: the Federalist Party and the Democratic-Republican Party. The duel between Alexander Hamilton and Aaron Burr, which lead to Hamilton's death, epitomized the bitterness between the two parties and demonstrates that hard emotions and political differences have a long history in the United States. Bitterness aside, two strong competing political parties is better than a single party because it prevents hegemony on ideology. When that happens we see violent discrimination. Single party states have a history of using secret police--e.g. Gestapo--to root out and systematically encourage discrimination against politically and culturally different others. Intolerance of difference is freedom's enemy.
2. It's a demonstration of personal insecurity.
If we can't handle a different point of view then we must not be entirely comfortable with our own point of view.
Social psychology has long recognized the power of cognitive dissonance on both our attitudes and our behavior. Cognitive dissonance occurs when we face two incongruent thoughts--this causes us to feel uncomfortable. For example: if you believe in creationism and then watch a persuasive presentation on evolution, you would likely experience cognitive dissonance. When this happens there is a need to resolve the discrepancy. If the evidence is compelling then the logical choice is to change positions. The history of cognitive dissonance research, on the other hand, suggests that we're more likely to double down on our position than we are to change our mind--especially if the issue is dear to us. Another strategy is to avoid things that create cognitive dissonance such as people with different religious or political views. Avoiding situations that challenge our worldview or denigrating the opposition implies our beliefs are too frail to face the opposition.
3. It defeats the political hope of positively influencing others.
If we truly believe our political views are correct then we want to influence other people. This isn't going to happen if we disassociate ourselves from people who are politically different. Doing otherwise demonstrates our insecurity because it suggests we're seeking reassurance. Yes, being with like-minded people helps galvanize beliefs but we're not really changing anyone's mind. While it's true that most people already have their mind made-up, if we're willing to talk, listen, and make concessions then more likely than not the other side will too. Little changes can make big impacts.
4. Relationships aren't single dimensional.
Most relationships aren't based on party affiliation or political orientation so why should they be threatened on that basis? Yes, some issues are pressing and the future is at stake. Notwithstanding, Americans with strong political bents have felt the future perilous since the Declaration of Independence. The other party has ALWAYS been wrong. The other party will always be wrong or it wouldn't be "the other party" and yet there has always been that other party. Maybe we should contemplate that fact before issuing threats or punishments for political difference. Is it worth loosing a friend over?