Are other countries Royal Family members treated with so much hate like "Meghan" and "Diana" were in their media and press?

It is not uncommon for members of the royal families to be criticised.  Some women who marry royalty manage to deal with the critics better than others. Even male members are not immune to attacks by the tabloids. 

Yes, other countries' royals face unfair criticism, especially women who marry into the royal families.

Mary McDonald, the Australian woman who married the Crown Prince of Denmark, was the target of extremely vicious attacks for years, and Crown Princess Mette-Marit of Norway and Princess Mabel of the Netherlands had to put up with rather a lot.

It's actually something of a tradition for women who marry into royal families to be attacked. It's been going on for centuries.

As I've posted recently, the Duchess of Cambridge and her family were also quite nastily targeted for years, until the tabloids got a new victim in their sights.

Diana was loved by the people, she had a love hate relationship with the media. Markle on the other hand is not very popular! 

Diana and Meghan both made the mistake to believe that they were popular for themselves and not for their roles.

You can't compare Diana and Megan. Impossible.  It's like comparing roses and thistles. Diana was much loved for her vast charity work and generosity. She was lovingly called the People's Princess.

As for the Mountbatten's fear of the media, it's kind of silly, considering who they are and who Princess Diana and Prince Charles were. Harry seems to have lost perspective.