To be fair, everyone from Chad to Sudan to the Horn had similar traditional attire. There were obviously unique regional variations like the alindi among Somalis but, for example, one thing that was universal was this obsession with white robes similar to Greco-Roman togas:
So an Oromo would not be wrong to claim our traditional attire is similar to theirs but I think the alindi designs you see among them and some other groups in the Horn and Kenya is just something that spread recently from Somalis though I might be wrong.