Ive seen a LSE guy and IEI girl interract quite a few times. Im not 100% sure of the girls type but pretty sure. From my experience there didn't seem to be a great deal of conflicting, it seemed quite toned down. Same with SEI and LIE. Ive asked them if they could see the conflictor relation, LSE had no idea what i was talking about and IEI i think said she could a little. LIE said he could definately see it but it doesn't stop him going to the movies with him?? I think perhaps theres an element with your conflictor where you know not to argue because it is going to turn ugly, almost a slight fear. Once that barrier passes it sucks.
Nothing like my conflictor relations with LSI's, but thats been fostering over years