This isn't going to be a problem for the RF - they managed to host Wallis Simpson for the Duke of Windsor's funeral. Prince Phillip even escorted her from the church (although I seem to remember the Queen Mother glaring a bit at her back).
The problem is going to come from the Sussex sense of entitlement if they demand being "equal" to the new King William. We saw this when the Queen died - having refused to visit the Queen in her final days they spent a lot of time complaining to their preferred media outlets - demanded that Meghan travel to Balmoral, complained that by the time Harry finally arrived Charles and William had been taken for briefings on affairs of state, whined that Harry couldn't dress up in a fancy uniform, snapped at staff because Meghan had set up a money shot with the paps on the Windsor walkabout .... It must have been exhausting for her grieving children and family members.
I expect Harry will be invited to the funeral, But I also expect there will be a tight rein on any interactions with officials and family members acting as a buffer. Remember that Charles didn't choose to have Harry in the front row at his Coronation so why would his funeral be different?