I don't know if Korean society is really like how it is portrayed in the drama since you want some rec. so here are some list.
Gender Inequality/Gender/Sexuality:
The Painter of the Wind
Goddess Of Fire, Jeongi
One Well-Raised Daughter
Coffee Prince
Wealth Gap:
Yong Pal
Ugly Alert
The Master's Sun
Shopping King Louis
Secret Garden
Save the Last Dance for Me
Protect the Boss
My Lovely Sam Soon
King2Hearts - (it also involve some politics)
Fated to Love You
Discrimination:
One Well-Raised Daughter
D-Day
Doctor Stranger
Yong Pal
Dream High
Ugly Alert
The Painter of the Wind
The Greatest Love
She Was Pretty
King2Hearts
Kill Me, Heal Me
Jealousy Incarnate
Hyde, Jekyll, Me
Goddess Of Fire, Jeongi
Academic Achievement/Struggles, Business, Work/Profession:
Cheese in the Trap
Heart to Heart
Dream High
You're All Surrounded
Hyde, Jekyll, Me
Hotel King
Hwang Jin Yi
Pinocchio
Kill Me, Heal Me
King of Baking, Kim Tak Goo
Lucky Romance
Romantic Doctor, Teacher Kim
Witch's Romance
Weightlifting Fairy Kim Bok Joo
Uncontrollably Fond
That Fool
Surplus Princess
Signal
Descendants of the Sun
Shopping King Louis
Protect the Boss
SK upholds traditions and history:
The King's Face
Empress Ki
The Eccentric Daughter-in-Law
Queen Seon Duk
Dong Yi
-And- there are some you might like:
Biscuit Teacher and Star Candy
Birth of a Beauty
Flower Boy Next Door
Goblin
Gu Family Book
Healer
I Hear Your Voice
I Remember You
Iljimae
Miss Granny
Ode To My Father
Oh My Venus