One place says closed Sat & Sun which just sounds wrong to me! Then it says most popular time Sunday. Then it says closed. ?? What gives? Is at or isnt it open on the weekend?

They are open every day

It is confusing. But they are open on the weekends. I had also seen something on some website that said they closed at 4:00 p.m. But that is not true either they close at sunset

Use the information at the Wildlife Refuge website which states they are open 7:30 am to sunset every day. There are COVID restrictions in place. Volunteers and rangers are staffing tables some days. https://www.fws.gov/refuge/Pelican_Island/visit/rules_and_regulations.html