Understanding Febrile Seizures “Febrile” means “relating to a fever.” In some children, having a fever—even fever that comes with typical childhood illnesses like ear infections or the common cold—can bring on a seizure. Measles was a common cause of febrile seizures in the United States before the disease became rare due to the success of the vaccination program. During a febrile seizure, a child often has spasms or jerking movements and may lose consciousness. Febrile seizures usually last only a minute or two. They are most common with fevers that get up to 102°F (38.9°C) or higher, but can also occur at lower temperatures or when a high fever is going down. Febrile seizures often result in a visit to an emergency room for the child and can be very frightening for parents and caregivers. However, most children who have febrile seizures recover quickly and have no lasting effects.
Which implies to me that the problem is MMR can cause a fever, and fevers can result in febrile seizures.
You should think really hard before trading off this risk for the increased risk of measles and mumps. Rubella I'm not so sure about (I think the #1 reason for that is to protect pregnant women).