Turn off the ability to use the custom color picker in the WordPress Gutenberg editor. Then, define your own custom color palette.

wp-custom-color-pallete-front-end.css

/* Define Custom Colors on the Front End */

/* white */
.has-white-color {
  color:#FFFFFF;
}
.has-white-background-color {
    background-color:#FFFFFF;
}

/* black */
.has-black-color {
  color:#000000;
}
.has-black-background-color {
    background-color:#000000;
}

/* yellow */
.has-yellow-color {
  color:#ffd000;
}
.has-yellow-background-color {
    background-color:#ffd000;
}

/* blue */
.has-blue-color {
  color:#347ab7;
}
.has-blue-background-color {
    background-color:#347ab7;
}

/* green */
.has-green-color {
  color:#2e924d;
}
.has-green-background-color {
    background-color:#2e924d;
}

/* gray */
.has-gray-color {
  color:#464646;
}
.has-gray-background-color {
    background-color:#464646;
}

/* light gray */
.has-lightgray-color {
  color:#ebebeb;
}
.has-lightgray-background-color {
    background-color:#ebebeb;
}

wp-custom-color-pallete.php

// Editor Color Palette
	add_theme_support( 'editor-color-palette', array(
            array(
                'name'  => __( 'White', 'textdomain' ),
                'slug'  => 'white',
                'color'	=> '#FFFFFF',
            ),
	      array(
                'name'	=> __( 'Black', 'textdomain' ),
                'slug'	=> 'black',
                'color'	=> '#000000',
            ),
            array(
                'name'  => __( 'Yellow', 'textdomain' ),
                'slug'  => 'yellow',
                'color'	=> '#ffd000',
            ),
            array(
                'name'  => __( 'Blue', 'textdomain' ),
                'slug'  => 'blue',
                'color' => '#347ab7',
            ),
            array(
                'name'  => __( 'Green', 'textdomain' ),
                'slug'  => 'green',
                'color' => '#2e924d',
            ),
            array(
                'name'	=> __( 'Gray', 'textdomain' ),
                'slug'	=> 'gray',
                'color'	=> '#464646',
            ),
            array(
                'name'	=> __( 'Light Gray', 'textdomain' ),
                'slug'	=> 'lightgray',
                'color'	=> '#ebebeb',
            ),
        ) );

wp-disable-custom-colors.php

// Disable Gutenberg Custom Colors
add_theme_support( 'disable-custom-colors' );

// Disable Gutenberg Custom Gradients
add_theme_support( 'disable-custom-gradients' );