好きなようにさせて

let [someone] do as they like

→ 好きだ
phrase Rare #30,548
let [someone] do as they like 好きなように means “as one likes,” and させて means “let [someone] do.” The person being allowed to act is usually clear from context.
JA: 今日は彼に好きなようにさせてあげよう。
EN: Let him do as he likes today.

あいつやはり好きなようにさせておけ

Just let that guy do whatever he wants, after all.

— もののけ姫 (1997)

トムの好きなようにさせてやりなさい。

Let Tom do as he pleases.

彼の好きなようにさせておいた方がいい。

It’s probably best to let him do things his own way.

いいか、世間に好きなようにさせている飽きるまでね

Listen, I’m letting the world do as it pleases until it gets bored.

— ラ・ラ・ランド (2016)