Well, in both cases you have the word had, which is past tense. Just because you put a verb there that does not mean it's in the current state. Other things indicates that. "Had a fall-out with each other" Fall out means a quarrel, to leave, to happen and to occur. A verb and many languages indicates occurrence. You could use the verb falling or you could say "fall-out", they both talk about an occurrence. They are having a huge fall-out. Meaning that they are still quarreling. It's all about how you set the sentence up. Certain phrases are past and present also. If they stopped associating with each other I think had is better to use than have. I think both of them are correct due to the tense of "fall-out"

a fall out= a disagreement