Freedom (including the choice to hate and like whatever you choose) is the premise that democracy is built on. Stopping certain groups from participating in the government simply because they have a certain opinion, negative or otherwise, is completely taking away and undermining this freedom. Democratic government is a representation of what the people of a country support, and if they support hate then so be it.
A nation wouldn't be very democratic if a group of people were completely removed from their own government simply because they have a negative view point. All have a right to speak their opinions (just look at this very website we are currently discussing this on) regardless of the message.
And as a side note, the freedom of speech that my fellow americans love so much is designed to defend unpopular speech. If the speech is popular, then it doesn't need the US government telling people that they have the right to speak it (because its popular and most agree with it). Its the ones that most don't agree with that need defending.
We live in a free nation, a nation based upon the will of the people. If the people like a certain group, then who are you to say that they are not justified? We need to accept that people in this nation get to choose whom they want to lead them, and if you don't like it then don't vote for them.
Based on the picture that was posted in reference to the question, than my answer is No. But, hate is a vague word. If someone hates a certain type of music, would you label that person as an outcast? If somebody hates a certain type of food, you wouldn't poke fun at that person, would you?
It shouldn't matter if your political party stands for other particular views like socialism or the constitution, if your party is based on a common hatred that has had genocidal and dehumanizing tendencies it should not even be legal. If you rallied a group on committing homicide you would be arrested for planning the murder so why should planning death of a mass group of people be different?