I don't mean algebraic geometry and all that. I seek a no nonsense introduction to string theory in terms of algebraic quantum field theory.
String theory doesn't obey the axioms of algebraic quantum field theory and, sociologically speaking, string theorists do not think that algebraic quantum field theory is a promising path anywhere, so you won't find any credible texts on string theory based on algebraic quantum field theory.
The perturbative string theory calculations are based on two-dimensional conformal field theories and they allow calculations of the "bootstrap" type and for similar reasons, the situation may be considered analogous to algebraic quantum field theory, too. But the precise formalism promoted by the actual champions of algebraic quantum field theory isn't usable in string theory.
It isn't really usable in modern quantum field theory, either. The logic behind the existence of divergences etc. was really revised in the 1970s. Algebraic quantum field theory was an older attempt than the Renormalization Group of the 1970s and it was realized that it was incorrect on many important assumptions.