Thawing conditions are unpredictable months before. Going there now is not a problem for an expedition with prepared vehicles. They even cross vatnajokull under good conditions, going to Landmannalaugar is much more easy.
The question wasn’t for just going there. 8th of June may be the period of snow melting and thawing. During this period no vehicle are allowed. Not even prepared ones, so long it is not dry enough. Passing is not the issue. Long term state of the FRoad is.