Electrons split in Stern-Gerlach experiment but not in Thompson's experiment?
As has already been suggested by some of the comments to your question, there is a fundamental difference between a Stern-Gerlach-type experiment and a Thompson-type experiment, and this difference lies in the type of interaction of the particles.

First of all, as Ivan Neretin points out, a Stern-Gerlach experiment is performed with neutral species (the original experiment involved silver atoms), while Thompson's experiment employed a beam of charged electrons. 

The Coulombic or Lorentz interaction between charged particles (or charged particles and fields) is rougly four orders of magnitude larger than the interaction between neutral particles and fields. In the latter case, one can have interaction between a magnetic dipole moment and a magnetic field and/or interaction with a electric dipole moment and an electric field. These interactions are referred to as Zeeman and Stark effects. The important thing to realize is that the sign and magnitude of the interaction depends on the quantum state of the particle (or in other words on the relative orientation of its angular momenta). It is therefore a quantum-state specific interaction. As a consequence particles in one state may be attracted to a region with high fields, while particles in another state may be attracted to regions with low fields, as if you have two different compasses; one that points to the North pole and one that points to the South pole.

Electromagnetic interactions between charged particles and fields are so strong that the quantum-state specific effects are much harder to see (and the Coulomb and Lorentz forces dominate).

Let's go back to the Stern-Gerlach experiment. In their experimental setup, Stern and Gerlach used an inhomogenous magnetic field with a well-defined gradient. The silver atoms they employed have one unpaired electron that could be oriented with respect to the external magnetic field "up" or "down", these different quantum states experience different forces and are therefore separated. 

In Thompson's experiment charged electrons are send through a magnetic field where the force they experience only depends on their charge and velocity vector with respect to the magnetic field. This force is identical for all electrons, so no splitting is observed.