好きなようにさせて

let me/them do as they like

→ 好きだ
phrase Rare #29,162
let me/them do as they like Used to ask or tell someone to let another person act as they please. The person being allowed to act is often understood from context; させて can make this sound like a request such as “let me...” or “leave them to it.”
JA: 彼女には好きなようにさせてあげて。
EN: Let her do as she likes.

トム好きなようにさせてやりなさい

Let Tom do as he pleases.

好きなようにさせて置け.

Leave him to do as he pleases.

— もののけ姫 (1997)

いいか世間に好きなようにさせている飽きるまで

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

— ラ・ラ・ランド (2016)

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.