The Islamic Relief USA organization has only existed for 17 years, which itself would be stretch to say “decades”.
And so far as I can tell from research, the LDS church’s first work with the IR-USA group was in 2004.
And the answer to your question appears to be that both organizations exist to aid people in crisis situations, and find it easier to help when they work together.
If I were an LDS member, I might have questions about my church associating with IR-USA. As an outside observer, I can’t see why people are upset that two organizations they are not involved with, and apparently would not ever BE involved with, are together providing aid and assistance to people in crisis in Haiti.