Ok this is a tough one considering a lot of anime don't even mention parents or they are never around. So I had to compile from the ones that do.
Ok so I will start with how my Parents are and how they view anime. Pretty obvious they don't really get it. But I noticed alot of parents in anime don't get their kids either.
some anime parents are actually very encouraging of their kids and push them onward through the plot of the anime.
While others may push them away or try and stop them from reaching their goals.
Of course I cannt ignore the fact that some characters lost their parents usually at a young age. so they have little to no memory of them. It's really tragic.
Of course I give a shout out to all those Single parents out there who are very Protective of their kids. Anime parents usually have alot more to worry about tho (like Hollow, aliens, and much much more).
Then we have to remember that they are a couple and do couple things. But like our parents we tend to wanna stay out of their love life.
Anime parents have no problem showing us who gets to be in their children's life though. They can be very Protective about others being with their children. Then you have the parents that aren't afraid to ask the awkward questions like "Is that the newest edition of 'playboy'?"
Of course anime parents worry about their children too and yell at them. (Usually for their own good.)