The wild bogeyman dropped his bag in the bank (5)
BOGEYMAN - dropped BAG = OEYMN, wild OEYMN = bank: MONEY.
God returned the small animals (4)
GOD returned = DOG + small (S) = animal: DOGS.
The insect stayed in the hospital and became a family member (6)
Thanks to @M Oehm for this parsing: The insect (MOTH) stayed in the hospital (ER) and became a family member = MOTHER.
I'm in half a byte of a magazine (4)
IM in half a by(T__E) = a magazine: TIME.
Colors of the music (5)
@Chris Cudmore has what I believe to be the correct parsing for this, colors = BLUES which also relates to music: BLUES.
D O G S
M O T H E R
B L U E S
I’m not at all sure about the theme here, because
Thanks to @jafe (because I only knew one of these songs), all answers are songs by Pink Floyd!