This is a perennial question for membership organizations like yours, or for umbrella organizations or other coalitions.  It can be a conflict, but it doesn’t have to be.  United Ways and similar organizations have struggled with this issue for years.

My favorite question about nonprofit organizations is “whose organization is it?”  A membership organization is usually controlled by its members.  Your statement that “they” have shown an interest in fundraising for “their organization” suggests that you don’t quite feel the organization is yours.  But if you vote to elect the directors, you have a direct influence on this decision. 

Even if you don’t vote, the “member” organizations should get together to determine whether you want the statewide group to solicit.  The statewide may be able to solicit for multiple agency demonstration projects, or research money, or other things that the locals don’t have the capacity to go after.  The statewide probably ought not go after funds in competition with the locals unless it has a greater solicitation capacity and will share the results.  There is no single appropriate answer to whether, or how, the statewide should solicit contributions, but it should be up for discussion if “they” intend to start something new that the members don’t like.