For my project we have to make a claim based off of how our country (mine is Libya) has been impacted by religion. Is this a solid claim:

Because of Libya’s transitional government, Mummer al Qaddafi came into power, leading the Libyan people in a government that was heavily influenced by Islam, mixing politics and religion together which caused the country to fall into turmoil.

It seems a valid claim, yes. You'll have to demonstrate that religious restrictions on the people of Libya were among the reasons some rebelled and brought about the chaos.