There is a slight difference that the verbs embody in virtue of their primary sense. If you have to know if someone adheres to a striking action you use “faire”, which connotes the act of participating willingly in, joining in the movement.

• — Tu vas faire grève toi ? (“être” is not at all possible.)
  — Je ne sais pas, je ferai (la) grève si je peux être convaincu avant le jour où elle a lieu.

Otherwise, when referring to a group of people on strike you can use both forms and anyone will understand that the group is on strike. “S’il font grève, eh bien c’est qu’ils sont en grève et vice versa.”.
What factually translates “to be on strike” is nevertheless “être en grève”.

Être en grève would explain a state, which is pretty easy to translate with be auxillary in English. This is a state a one person or a group of person, and there is a lot of example that works like that :

• être malade e.g to be sick
• être en retard e.g to be late

However, Faire grève is an action, that would be easier to translate with do or make auxillaries (which are not the case here). Also, there is a lot of example that could represent an action :

• faire un embouteillage e.g to make a traffic jam (protesters loves to do that in France)
• faire un gâteau e.g to do a cake

NB : faire grève would be better translated as to strike, and also fairelagrève as to go on strike (both are actions, just said with differents way)