I could really get into this. The Stark had other issues. One, keep in mind that the Exocet RCS (radar cross section) is very small. So that makes it very hard to see with radar, espcially with the SPS-49 radar. So the ability to see skin seperation from the F-1 was more than likely not seen by the operator. Then, also, especially in mid 80's, ships did not run the CIWS in full auto and probably still don't to this day. This is not to mention the SLQ-32 ESM operator would have a very short reaction time once Exocet radar lit off. So with all of our expensive systems to keep ships safe, a $30k missile can pretty much ruin your day.
Also, Iraq was our friend then, and who shoots at their friend?