This JSOM code snippet enables the access to users to customize the master pages and page layouts in the current site collection level.

enableMasterPageAccess.js

//Author: Shantha Kumar T
//Property used: SP.Site.allowMasterPageEditing (sp.js)
//Supports SharePoint 2010 + and SharePoint Online

function enableMasterPageAccess() {
    var clientContext = new SP.ClientContext();
    oSite = clientContext.get_site();

    //The below line helps to enables the master page access
    oSite.set_allowMasterPageEditing(true);

    clientContext.load(oSite);
    clientContext.executeQueryAsync(
        Function.createDelegate(this, function() {
            var siteInfo = '';
            //The below line get the boolean value of  master page editing is allowed on this site collection
            if (oSite.get_allowMasterPageEditing())
                siteInfo = 'MasterPage customization: Allowed';
            else
                siteInfo = 'MasterPage customization: Not Allowed';
            alert(siteInfo.toString());
        }),
        Function.createDelegate(this, function(sender, args) {
            alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
        }));
}

function injectMethod() {
    enableMasterPageAccess();
}
ExecuteOrDelayUntilScriptLoaded(injectMethod, "sp.js");