Is there a saying in English that basically means "adapting to your target audience"?

Solution 1:

Perhaps trim one's sails to the wind

make changes to suit one’s new circumstances.

The phrases

• play to the crowd
• play to the gallery
• play to the audience

are also used to mean

to perform in a manner that will get the strong approval of the audience; to perform in a manner that will get the approval of the lower elements in the audience.

Solution 2:

There's one expression in British English which is similar in meaning. We speak of horses for courses.

Solution 3:

"serving the syrup according to the arteries" (quite literally translated).

https://idioms.thefreedictionary.com/cut+your+cloth To cut one's cloth according to the/its width. This is mainly British English and indicates adapting your material (in its widest sense) to the circumstances.