gistfile1.xml

<?xml version="1.0" encoding="UTF-8"?>

<cdk:root xmlns="http://jboss.org/schema/richfaces/cdk/xhtml-el" xmlns:cdk="http://jboss.org/schema/richfaces/cdk/core"
    xmlns:c="http://jboss.org/schema/richfaces/cdk/jstl/core" xmlns:cc="http://jboss.org/schema/richfaces/cdk/jsf/composite">

    <cc:interface>
        <cdk:class>org.richfaces.bootstrap.renderkit.CommandButtonRenderer</cdk:class>
        <cdk:superclass>org.richfaces.bootstrap.renderkit.CommandButtonRendererBase</cdk:superclass>
        <cdk:renderer-type>org.richfaces.bootstrap.CommandButtonRenderer</cdk:renderer-type>
        <cdk:renders-children>true</cdk:renders-children>
        <cdk:component-base-class>org.richfaces.bootstrap.component.AbstractCommandButton</cdk:component-base-class>
    </cc:interface>

    <cc:implementation>
        <cdk:object type="String" name="type"
            value="#{'client' eq component.attributes['mode'].toString() ? 'button' : component.attributes['type'].toString()}" />

        <c:choose>
            <c:when test="#{component.hasFacet('split')}">
                <cdk:renderFragment name="renderSplit" type="#{type}" />
            </c:when>

            <c:otherwise>
                <cdk:renderFragment name="renderCommandButton" type="#{type}" />
            </c:otherwise>
        </c:choose>
    </cc:implementation>

    <cdk:fragment name="renderCommandButton">
        <cc:interface>
            <cc:attribute name="type" type="String" />
            <cc:attribute name="split" type="boolean" default="false" />
        </cc:interface>

        <cc:implementation>

            <cdk:object name="styleWhenNotSplit" type="String" value="#{!cc.attrs.split ? component.style : ''}" />
            <cdk:object name="styleClassWhenNotSplit" type="String" value="#{!cc.attrs.split ? component.styleClass : ''}" />
            <cdk:object name="severityClass" type="String"
                value="#{component.severity ne null ? component.severity.buttonClass : ''}" />
            <cdk:object name="scaleClass" type="String" value="#{component.scale ne null ? component.scale.buttonStyleClass : ''}" />
            <cdk:object name="color" type="String" value="#{component.color}" />
            <cdk:object name="colorStyle" type="String" value="color: #{color};" />
            <cdk:object name="colorStyleWhenNotEmpty" type="String" value="#{color ne null and !color.equals('') ? colorStyle : ''}" />

            <c:choose>
                <c:when test="#{component.tag eq 'button'}">

                    <!-- Button -->
                    
                    <button name="#{clientId}" value="#{component.value}" class="btn  #{styleClassWhenNotSplit} #{severityClass} #{scaleClass}"
                        style="#{styleWhenNotSplit} #{colorStyleWhenNotEmpty}" onclick="#{this.getOnClick(facesContext, component)}"
                        cdk:passThrough="title ondblclick onmousedown onmouseup onmouseover onmousemove onmouseout disabled"
                        type="#{cc.attrs.type}">

                        <cdk:call expression="encodeId(facesContext, component, split, clientId);" />

                        <c:if test="#{!empty(component.icon)}">
                            <i class="icon-#{component.icon}"></i>
                            #{" "}
                        </c:if>

                        #{component.value}

                        <cdk:call expression="renderChildren(facesContext, component);" />

                    </button>
                </c:when>
                
                <c:when test="#{component.tag eq 'input'}">
                    
                    <!-- Input -->
                    
                    <input type="submit" name="#{clientId}" class="btn #{styleClassWhenNotSplit} #{severityClass} #{scaleClass}"
                        style="#{styleWhenNotSplit} #{colorStyleWhenNotEmpty}" value="#{component.value}"
                        onclick="#{this.getOnClick(facesContext, component)}" cdk:passThrough="title ondblclick onmousedown onmouseup onmouseover onmousemove onmouseout disabled">

                        <cdk:call expression="encodeId(facesContext, component, split, clientId);" />
                        <cdk:call expression="encodeTypeAndImage(facesContext, component);" />

                    </input>

                </c:when>
            </c:choose>
        </cc:implementation>
    </cdk:fragment>



    <cdk:fragment name="renderSplit">
        <cc:interface>
            <cc:attribute name="type" type="String" />
        </cc:interface>

        <cc:implementation>

            <cdk:object name="severityClass" type="String"
                value="#{component.severity ne null ? component.severity.buttonClass : ''}" />
            <cdk:object name="scaleClass" type="String" value="#{component.scale ne null ? component.scale.buttonStyleClass : ''}" />
            <cdk:object name="color" type="String" value="#{component.color}" />
            <cdk:object name="colorStyle" type="String" value="border-top-color: #{color}; border-bottom-color: #{color};" />
            <cdk:object name="horizontalClass" type="String"
                value="#{component.horizontal ne null ? component.horizontal.buttonClass : ''}" />


            <div id="#{clientId}" cdk:passThrough="style"
                class="btn-group #{component.styleClass} #{component.vertical ne null ? component.vertical.buttonClass : ''}">

                <cdk:renderFragment name="renderCommandButton" type="#{type}" split="true" />



                <button data-toggle="dropdown" class="btn dropdown-toggle #{severityClass} #{scaleClass} ">
                    <span class="caret" style="#{color == null ? '' : colorStyle}"></span>
                </button>

                <ul class="dropdown-menu #{horizontalClass}">
                    <c:forEach var="child" items="#{component.getFacetChildren('split')}">
                        <li>
                            <cdk:call expression="child.encodeAll(facesContext)" />
                        </li>
                    </c:forEach>
                </ul>
            </div>
        </cc:implementation>
    </cdk:fragment>
</cdk:root>

(I wanted to say the "style" attribute in the 1st point)

Okay, great, I have made the changes you mentioned and pushed that upstream.