They are indeed very sensitive, or should I say, sort of reactive and volatile when upset?
My sister is ESFJ, I have an xSFJ close friend, and I know an ESFJ who has tried to start a relationship with me twice now.
I've always gotten along with them by being sensitive to their needs and showing appreciation for them. They also tend to want someone to listen to them and care about them for once, and I fulfill that role quite nicely.
Basically, look out for their needs and be kind and gentle in your communication with them. Yes, they are super sensitive, but also can be very reasonable when you show that you're inclined to listen to them as they sort through any issues.
You need to ride out that first flash of anger/upset, and then approach them when they've simmered down a little. They will notice and appreciate your approach because that is a strong indicator that you care.