And I couldn't find any example of SOC being considered for Magnetic systems.
There are many examples that consider the effect of SOC in magnetic systems. For example, the monolayer LaBr$_2$ in this paper, in which the author compares the band structures for three cases as follows:

A bulk case also could be found in this paper: Phys. Rev. Lett. 122, 206401
So is it necessary to start with a starting_magnetization of zero for magnetic systems while considering SOC?
In short, the answer is NO.
The magnetic materials usually are calculated with spin-polarized mode (collinear), in which the electrons are classified into spin-up and spin-down and you only assign the initial magnetic momentum for each atom (just a number).
However, for magnetic materials with heavy atoms, you should do the noncollinear magnetic calculations,for magnetic materials with heavy atoms, you should do the noncollinear magnetic calculations, in which you should open the tag of SOC and set the initial magnetic momentum for each atom (a $1 \times 3$ vector) at the same time.
You may take a look at the explanation about the initial magnetization in vaspwiki.
For QE, you could take a look at the following tutorial to do noncollinear magnetic calculations:
May it helps.