Nope, no problem. There are no restrictions for Mormons regarding meat. We do however have guidance regarding alcohol, drugs, tobacco, coffee and tea. Here is a good, quick overview of the commandments we believe God has given us to help us: http://mormon.org/commandments/

There is no restrictions on eating the meat of animals with split hoofs in the Church of Jesus Christ of Latter-day Saints.  
 
These temporal laws were fulfilled (which included the Law of blood sacrifice) were all fulfilled when Jehovah the Great I am, came to Earth as the Only Begotten Son of the Father and sacrificed his perfect and immortal self for the sins of the entire world. When this happened the temple veil of the temple was torn into two and it is believe that they arc of the covenant was destroyed to show that the old Mosaic laws were fulfilled that the price for sin had been paid and mankind is reconciled with God through the Son our mediator and our savior.  
 
 
We are not without modern guidance for our times though, in the Doctrine and Covenants which contains modern revelations to the Prophet Joseph Smith (the founder of our faith) we are given various instructions regarding nourishment.  
 
In regards to animal and meat we are told that meat is good for the body but is to be used sparingly and that all things need to be in moderation. We are also prohibited from consuming tobacco, alcohol, tea, and coffee. We are stingily advised as well to avoid all addictive substances and behaviors REGARDLESS if they are explicitly prohibited by the doctrine of the Church.  
 
We believe that a healthy diet that is sparing in meat, plentiful in grains, fruits, and vegetables (but still in moderation for excess of any food is bad for the body) and absent of tobacco, alcohol, tea, and coffee is a recipe for a long, prosperous and healthy life.  
 
In fact many our or leaders contribute there longevity to there faithful obedience to the health commandments give by God to the Church of Jesus Christ of Latter-day Saints.

One factual error: the plaza on which the gay clpoue was kissing is PRIVATE property owned by the church, and so they can set what ever rules they want. When someone is asked to leave, as the clpoue was, and refuse they become trespassers and can be arrested or cited.