Is the equation below for Gibbs energy only applicable under standard conditions?
The equation as you wrote it refers to the standard state only. However, if you look at a system that is not at standard state, the relevant relationship looks very similar, dropping the standard state from both sides (the assumption then is that both refer to the same non-standard state that you are looking at at the moment): 

$$ \Delta G = -n F E $$

The same goes for relating Gibbs energy to enthalpy and entropy:

Both

$$ \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ $$

and

$$ \Delta G = \Delta H - T \Delta S $$

are correct. (Again, G, H, and S should refer to the same state in the lower equation.)

However, there are other relationships concerning Gibbs free energy where you have to be at standard state. For example,

$$ \Delta G^\circ = - RT \ln(K) $$

If you wanted a similar relationship for non-standard state, you have to account for it, e.g.

$$ \Delta G = - RT \ln\left(\frac{K}{Q}\right)$$

usually written as

$$ \Delta G = RT \ln\left(\frac{Q}{K}\right)$$


  This is quite confusing to me because it seems as if a lot of people use standard state equations and non standard state ones interchangeably.


If you have a correct relationship of Gibbs energy, enthalpy or entropy that is true for any state (i.e. written without the $^\circ$), you can always write the same equation specifically for the standard state by adding the $^\circ$ to all the state functions. The reverse (just dropping the requirement for standard state) is not always possible, as shown in the example above.