Help understanding external magnetic field sensitivity of radical pair reaction rate
(This is really a comment but  has become too long)
There are many examples of  triplet states in magnetic fields as studied by electron paramagnetic resonance (ESR or EPR) experiments. See chapter 8 'Introduction to Magnetic Resonance' by Carrington &amp; McLachlan. It is an old book but does contain all you need to know. (A paper I happen to know showing magnetic field effects is Hyde et al. Chemical Physics v151,p239 1991 but there must be many others if you search)

As to the bird experiments, eqn 1 of the paper by Schulten et al. as described in your question describes the situation: scheme copied below. 

$$\begin{align}
(D^*&amp;+A)\leftrightharpoons \;^1(^2A^-+\;^2D^+) \stackrel{B}\leftrightharpoons \; ^3(^2A^-+\;^2D^+)\to \;^3T\\ &amp;\downarrow\\ &amp;\;^1X \end{align}$$

What it seems is necessary is (a) The reaction starts with a light induced electron transfer from excited donor $D^*$ to a nearby molecule that is the acceptor $A$. (b) The singlet state $^1(^2A^-+\;^2D^+) $ species produced has energy levels that cross those of one of the  of $m_I=\pm 1$ levels of the triplet states $^3(^2A^-+\;^2D^+) $ three levels at some value of the magnetic field $B$ and so singlet to triplet crossing occurs($^1$). (c) This enables the yield of products $^3T$ to $^1X$ to vary as the value of the magnetic field varies as the animal moves. (d) The protein has to be fixed relative to the bird otherwise this will not work. (This is the 'anisotropy' mentioned)  Being fixed could simply mean being in a cell membrane in one part of the retina. (e) Somehow the ratio of products has to be able to be distinguished.  Clearly this mechanism clearly will not work at night. 

So all in all a complicated mechanism, involving subtle processes, and this makes it very interesting.



($^1$) In a molecule as the triplet often differs significantly in energy from the singlet a huge magnetic field is needed to reach the S-T crossing point, but in pairs of molecule the interaction is very small and so the energy difference is v small also. This is advantageous as then small magnetic fields can cause S-T crossing. (Normally the singlet is above the triplet in energy, unlike the in figure, but the crossing is clear nonetheless)

also see Can magnetic fields affect a chemical reaction?