Recommended color range for background color

I am building an online menu for restaurants.

The default background color is a light gray (#f1f3f5). The default text color is black (#555555). Example

Many of the restaurants have asked to use a custom color for the background. At first I said no, because users are not designers and use colors awfully... but after many requests I am starting to investigate a solution.

The idea is to allow the user to pick any color. Then the color is adjusted within a range.

In particular we would like to keep a light background with dark text on it.

So the solution was to use HSL and force L to a minimum of 0.9.

It has a sufficient effect, but I am not 100% satisfied.

Is there any study about the acceptable color range for a full-screen background (saturation, luminance)?