I believe this is the previous issue you mention in your post, Modify scheduler Day Header color

Further test indicate that in Week view and Month view, since the header will have dynamic style, the custom style will be overridden by the scheduler header style. For such scenario, you will need to create a HTML element, a DIV, in the header and move all the child node of the header to the newly created DIV. The style will be appended to this newly created DIV. Here is the modified snippet:

<style type="text/css">
    .customHead
    {
        background-image: none;
        background-color: Black;
        color: White;
    }
</style>
<script type="text/javascript" language="javascript">
    function WebScheduler1_OnAfterRenderView(controlId, viewMode)
    {
        var sched = ISGetObject(controlId);
        var headerElem = null;
        var type = "";

        //Setting all date 1 to have black background color with white text
        switch (viewMode)
        {
            case "Day":
                headerElem = sched.GetDayDayHeader().getElementsByTagName('td');
                type = 'DayHeader;';
                break;
            case "Week":
                headerElem = sched.GetWeekDayHeader().getElementsByTagName('td');
                type = 'DayHeader;';
                break;
            case "Month":
                headerElem = sched.GetSchedulerTableFrame().getElementsByTagName('td');
                type = 'MonthInboundDateHeader;MonthOutboundDateHeader;';
                break;
            case "Quarter":
                headerElem = sched.GetSchedulerTableFrame().getElementsByTagName('td');
                type = 'YearDayOfWeek;';
                break;
            case "Year":
                headerElem = sched.GetSchedulerTableFrame().getElementsByTagName('td');
                type = 'YearDayOfWeek;';
                break;
        }

        if (headerElem != null)
        {
            for (var i = 0; i < headerElem.length; i++)
            {
                if (type.indexOf(headerElem[i].getAttribute('type') + ";") != -1 &&
                headerElem[i].getAttribute('d') == '1')
                {
                    var innerContent = headerElem[i].innerHTML;
                    var childs = headerElem[i].childNodes;

                    var childCount = childs.length;
                    var loop = 0;

                    var newdiv = document.createElement('div');
                    newdiv.className = "customHead";
                    newdiv.style.height = headerElem[i].clientHeight + "px";
                    newdiv.style.lineHeight = headerElem[i].clientHeight + "px";
                    
                    while (loop < childCount)
                    {
                        newdiv.appendChild(childs[0]);
                        loop++;
                    }

                    headerElem[i].appendChild(newdiv);
                }
            }
        }
    }
</script>