I do not believe I have the authority to answer, because I don't know what exactly these anti-mormons are so... anti-mormon about. 
 
Most people who are simply against LDS don't have a correct understanding. Perhaps they are under the assumption of something that nobody's cleared up for them?

It all depends on why they are anti-Mormon. Some of those people either were once part of the Mormon faith, but later fell from their faith or were excommunicated from the Church. Unfortunately, they feel shunned from family and friends after leaving the LDS Church. Another group of people are Evangelical Christians (often are Biblical literalist) feel that Mormonism is a cult that they must get rid of by any means. 
 
However, from my experiences in Utah, Mormons are very accepting of other faiths in the state (feel they have just as much right to be there as they do) and the general US population holds little grudges to people of a different faith. Be nice to the people and they will be nice back. Many missionaries are understanding as well if you tell them that you are comfortable with your current beliefs and are not interested in investigation the Mormon faith. 
 
Don't feel that you need to hang around with anti-Mormons just because they share your religious beliefs (no one wants to hang around a negative person). Tell them thanks for the information, but you are not interested in hearing about Mormon beliefs.

You presented two very important questions! 
 
1) Is there any valid reason for the hate and loathing of Anti-Mormons toward Mormons? 
 
2)What are you missing that makes Anti-Mormons hate Mormons? 
 
1) Anti-Mormons have never had a single valid reason to hat or loath Mormons. Most are professed Christians so they should never hate, ever, period. In fact the hatred most Anti-Mormons show to Mormons tends to get people to investigate the LDS Church and helps us share our message of the peace and love of the Restored Gospel of Jesus Christ.  
 
2) The main reason behind Anti-Mormon hatred is two fold.  
 
a) Former members, since the foundation of the Church there has always been people who have left the Church angry for one reason or another. The most violently angered usually turn around and use there anger to preach against our Church, and do this to feel better about there selfish anger towards our peaceful organization.  
 
b) Those who fear our message.  
There are many Anti-Mormons who fear our message of a restored Gospel and how out people prosper in peace and happiness. Our prosperity and our message that we are the one true church is a threat to those looking for truth and happiness.  
 
In both cases they are not following the teachings of Christ but the false teachings of Satan.  
 
Christ never condones hate and slandering others. So if there message isn't based in Christ then they are based in the deceiver.  
 
Thank you WA for asking these two important questions and know that if you have any questions about the LDS Church mormon.org and lds.org have factual answers!