How do acids prevent ferrous sulfate from getting oxidised?
No, adding acid to a ferrous sulfate solution will not prevent its being oxidized by bromine water.
Fresh FeSO$_4$ solutions are light blue-green, almost colorless, but pick up O$_2$ readily:
Fe$^3$$^+$ + e$^-$ --&gt; Fe$^2$$^+$       +0.770 V and
O$_2$ + 2 H$_2$O + 4e$^-$ --&gt; 4 OH$^-$    +0.401 V
(The half cell voltages are only indicative of what's going on, because we are not at standard concentrations of 1 M.)
The light-colored solution quickly becomes yellowish and consumes all the oxygen in the vessel, and then sucks in more air and consumes that oxygen, and then things slow down a little, but diffusion still lets a bit more oxygen get in, and the &quot;ferrous&quot; becomes somewhat ferric, and the liquid becomes a muddy color and you wish you could preserve the nice blue-green color somehow.
You could preserve the ferrous if you could somehow complex it and keep it from oxidizing to ferric. But nature prefers to complex the ferric ion: smaller ion, bigger charge. Typical ferric stability constants are larger than ferrous by ten orders of magnitude.
It is instinctive to suppose that metals will oxidize in the presence of O$_2$, and if higher valences are possible, well, then, the metal will go as far as possible. But the oxidation of ferrous to ferric is unfavored (+0.770 V) and Fe$^2$$^+$ needs help from O$_2$. The reduction of water is also unfavored, but is driven forward by the consumption of OH$^-$ ions by precipitation by Fe$^+$$^3$, which also keeps the Fe$^+$$^3$ low.
LeChatelier predicted as much: by increasing the acidity, you reduce the availability of electrons from OH$^-$, and O$_2$ is more able to take electrons from Fe$^+$$^2$.
So you could say that adding acid stabilizes the ferrous ion, but what it really does is inhibit the oxygen molecule. Bromine is totally unaffected.