How does the CMB constrain the baryon asymmetry? The CMB contains information about baryon acoustic oscillations in which baryons (I assume protons and electrons) and photons form a plasma exhibiting sound waves. How is information about the baryon asymmetry of the universe contain in this?
Why do we not get some combination of baryon and (charged) lepton asymmetries if there are both electrons and protons in the mix?
Why does the dependence not go as their density but rather the asymmetry?
 A: Here is a description:

The acoustic oscillations arise because of a conflict in the photon–baryon plasma in the early universe. The pressure of the photons tends to erase anisotropies, whereas the gravitational attraction of the baryons, moving at speeds much slower than light, makes them tend to collapse to form overdensities. These two effects compete to create acoustic oscillations, which give the microwave background its characteristic peak structure. The peaks correspond, roughly, to resonances in which the photons decouple when a particular mode is at its peak amplitude. 

You ask:

How is information about the baryon asymmetry of the universe contain in this?

Please note the correction to the previous version of the answer, as I found a paper where the acoustic oscillations of the CMB are used in order to estimate the baryon asymmetry.
They have a phenomenological model of how more matter and  antimatter annihilation  gamma rays would affect the acoustic oscillations  at photon decoupling to give the CMB

at 380.000 years after the Big Bang, where it says transparency point for light, where the photons of the CMB have their last scatter before reaching our detectors.
These oscillations depend on the density of matter previous to the CMB , according to their model, the existence of an asymmetry can be found from the oscillations. Baryon antibaryon's annihilating would affect by the gamma rays generated the final photon spectrum at photon decoupling time.
The subject is still at a research state.
