The workaround is to use the RadEditor's tab functionality instead of browser's.

<telerik:RadEditor ID="RadEditor1" runat="server" OnClientLoad="OnClientLoad">
    <Content>
        <p>test</p>
        <p>test</p>
    </Content>
</telerik:RadEditor>

<script>
    function OnClientLoad(editor, args) {
        var shortcutManager = editor.get_shortCutManager();
        if (shortcutManager.findShortCutByName("InsertTabMozilla")) {
            shortcutManager.removeShortCut("InsertTabMozilla");
            editor.addShortCut("InsertTab", "TAB");
        }
    }
</script>