I was a long time LLL leader...for about 11 years. I stopped being a leader when I became a IBCLC, and also an apprentice Midwife. The area I lived in was very against Leaders becoming IBCLC's, or maybe it was just an area adviser. However, about two years after I retired, it was realized that there was definitely a place for LC"s who were willing to volunteer, as well as earn wages, within the group.
I suspect this is a similar situation. One person has an idea of what the group should be. It is however, very important within LLL that other "platforms" are not supported, and that everyone feels that they can be encouraged to breastfeed. As a result they do not promote politics, religion or any other specific causes.
Becoming a homebirth midwife is am important goal and may not be a problem with LLL, providing you do not tell everyone that homebirth is the only way to go. I guess the way to go is to support everyone to breastfeed, so that they can become empowered enough to ask about birth and other alternatives. I must admit that this certainly happened to me.
So, think about what you can get from the organization, what you can give to the organization, and if you will really have to give anything up to become a leader.