Do they?
I haven't been to LDS Church (other than family sponsored events) for over 20 years.
You see them all the time on tv, here in CA at the A&E church we saw Clinton, Kerry, and all the rest of the left.
According to reports during Vincente Fox's visit there last month, the church is a huge supporter of illegal immigration. Has a lot to do with increasing the mormon population in Mexico, which is the fastest growing religion there.... I found it very interesting to learn Mitt Romney's family is from Mexico and he still has a lot of relations there.