Baptists are a mix of beliefs.Yes. A lot of Reformed folks do not accept the idea of there being any such thing as "Reformed Baptists". I think it's pretty common nowadays for people to sort of pick out beliefs in a cafeteria style. A lot of folks in Reformed Baptist churches in the pews do not believe in limited atonement for example. Get on the internet and look at the "What We Believe" statements and most are very vague on that - leaving room for both on purpose. And it's not uncommon in Reformed Baptist churches to have cessationists and people waiting for the gifts to break out!
I believe that the Baptist part comes primarily from Anabaptist Theology. The reason is what we call the "Baptist distinctives" were a part of Anabaptist general belief. But Baptists picked those out while leaving behind what they didn't hold (different parts of their theology by different Baptist sects).
Baptists also took from the Reformers (again, what each sect saw as true). Some took Penal Substitution Theory from Calvinists. Some Satisfaction Theory from Luther. Others kept the Anabaptist understanding of the Atonement. Some took unconditional election. Others took free-will theology.
What has been lost today is Christian history. For some reason many Baptists have also taken the idea of "church" from the Catholics and look for a string of "true churches" throughout history which necessitates denying historic theological development.