custom chrome tabs asks for multiple browser to choose

Supporting multiple browsers

The Custom Tabs protocol is open, meaning that other browsers can support it. In fact, the Samsung Internet Browser already supports it (albeit with broken implementation) and Firefox has added an initial, very experimental support to it's nightly builds.

So, best practice would be querying the Android system on which of the installed browsers support the Custom Tabs protocol:

private static final String ACTION_CUSTOM_TABS_CONNECTION =
        "android.support.customtabs.action.CustomTabsService";

public static ArrayList<ResolveInfo> getCustomTabsPackages(Context context) {
    PackageManager pm = context.getPackageManager();
    // Get default VIEW intent handler.
    Intent activityIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("http://www.example.com"));

    // Get all apps that can handle VIEW intents.
    List<ResolveInfo> resolvedActivityList = pm.queryIntentActivities(activityIntent, 0);
    ArrayList<ResolveInfo> packagesSupportingCustomTabs = new ArrayList<>();
    for (ResolveInfo info : resolvedActivityList) {
        Intent serviceIntent = new Intent();
        serviceIntent.setAction(ACTION_CUSTOM_TABS_CONNECTION);
        serviceIntent.setPackage(info.activityInfo.packageName);
        if (pm.resolveService(serviceIntent, 0) != null) {
            packagesSupportingCustomTabs.add(info);
        }
    }

    return packagesSupportingCustomTabs;
}

You may want to check ResolveInfo#preferredOrder to check if the user has preference on one of the apps over the others. Also, if there's no preferred app (or two apps have the same major preference level), you may want to ask the user to choose one, or go with reasonable defaults

Thinking about Native apps

It is also important to check if the give Url has a native application that handles it installed. If so, it may make sense for your app to start the native one instead of opening it in a Custom Tab:

public static List<ResolveInfo> getNativeApp(Context context, Uri uri) {
    PackageManager pm = context.getPackageManager();

    //Get all Apps that resolve a random url
    Intent browserActivityIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("http://www.example.com"));
    List<ResolveInfo> resolvedBrowserList = pm.queryIntentActivities(browserActivityIntent, 0);

    Intent specializedActivityIntent = new Intent(Intent.ACTION_VIEW, uri);
    List<ResolveInfo> resolvedSpecializedList = pm.queryIntentActivities(specializedActivityIntent, 0);
    resolvedSpecializedList.removeAll(resolvedBrowserList);

    return resolvedBrowserList;

}

Opening the Custom Tab with an specific package

Once decided on which handler to use to open the Custom Tab, use the mCustomTabsIntent.intent.setPackage(packageName); to tell Custom Tab which application to open it.

Check this stackoverflow answer: if you set the CustomTabIntent package with the package of your desired browser before launch the url, you can skip the Android dialog browser choice; for me it worked:

/**
 * Opens the URL on a Custom Tab
 *
 * @param activity         The host activity.
 * @param uri              the Uri to be opened.
 */
public static void openCustomTab(Activity activity,
                                 Uri uri) {
    // Here is a method that returns the chrome package name 
    String packageName = CustomTabsHelper.getPackageNameToUse(activity, mUrl);

    CustomTabsIntent.Builder builder = new CustomTabsIntent.Builder();
    mCustomTabsIntent = builder
            .setShowTitle(true)
            .build();
    builder.setToolbarColor(ContextCompat.getColor(activity, R.color.colorPrimary));

    if ( packageName != null ) {
        mCustomTabsIntent.intent.setPackage(packageName);
    }
    mCustomTabsIntent.launchUrl(activity, uri);
}