lets put it like this though the royal family as an institution is held in a neutral regard by the general public
The Queen's Mother was massively popular throughout her life
The Queen herself is quite popular
Princess Ann does a significant amount of charity work behind the scenes
Prince William is a serving RAF rescue pilot
Prince Harry is a serving rifleman and had a short stint as a front line combatant in Afganistan (he would have served a full tour if it wasn't for stupid tabloids putting circulation above his and his fellow soldiers welfare.)
the only blots at the moment is Prince Charles sticking his 2 pence into subjects he isn't as well educated about as he should be and Prince Philip who is too old guard for his own good especially when it comes to foreigners