TSconfig

RTE.classes.tb-zebra-rows {
	name = Zebra rows
	alternating.rows {
		// first row is 1 (odd) not 0
		startAt = 1
		// odd tr in tbody
		oddClass = tr-odd
		// even tr in tbody
		evenClass = tr-even
		// odd tr in thead or .thead
		oddHeaderClass = header-odd
		// even tr in thead or .thead
		evenHeaderClass = header-even
	}
}

RTE.classes.tb-zebra-columns {
	name = Zebra columns
	alternating.columns {
		// first column is 1 (odd) not 0
		startAt = 1
		// odd td in tbody
		oddClass = td-odd
		// even td in tbody
		evenClass = td-even
		// odd th on top (either inside thead or tr.thead)
		oddHeaderClass = th-odd
		// odd th on top (either inside thead or tr.thead)
		evenHeaderClass = th-even
	}
}

RTE.default.buttons.blockstyle.tags {
	# table.allowedClasses = tb-zebra-rows, tb-zebra-cols
	table.allowedClasses = tb-zebra-rows, tb-zebra-cols, noBorder
	tr.allowedClasses = tr-odd, tr-even, header-odd, header-even
	# td.allowedClasses = td-odd, td-even
	td.allowedClasses = td-odd, td-even, noImage, status0, status1, status2, withImage, lightBg, darkBg
	th.allowedClasses = header-odd, header-even, th-odd, th-even
}

RTE.mutuallyExclusiveClasses {
	10 = tr-odd,tr-even,header-odd,header-even
	20 = td-odd,td-even
	30 = th-odd,th-even
	40 = tb-zebra-cols, tb-zebra-rows
}

RTE.default.proc.allowedClasses := addToList(tb-zebra-rows, tb-zebra-cols,tr-odd, tr-even, header-odd, header-even, td-odd, td-even, header-odd, header-even, th-odd, th-even, thead, noBorder, noImage, status0, status1, status2, withImage, darkBg, lightBg)
RTE.default.contentCSS = fileadmin/sitename/css/style_rte.css

CSS (style_rte.css)

table.tb-zebra-rows, table.tb-zebra-rows tr, table.tb-zebra-rows th, table.tb-zebra-rows td {
	border: none;
}

table.tb-zebra-rows td {
	border-right: 1px solid #FFFFFF;
}

table.tb-zebra-rows tr.header-odd, table.tb-zebra-rows tr.header-even {
	font-size: 14px;
	line-height: 16px;
	font-weight: normal;
	text-align: center;
	vertical-align: top;
	color: #7092B0;	
	background-color: #094880;
	padding: 3px 7px;
}

table.tb-zebra-rows tr.header-odd th, table.tb-zebra-rows tr.header-even th,
table.tb-zebra-rows tr.header-odd th p, table.tb-zebra-rows tr.header-even th p {
	color: #A8C0D6;
}

table.tb-zebra-rows tr.tr-odd {
	background-color: #FFFFFF;
}

table.tb-zebra-rows tr.tr-even {
	background-color: #EAECEE;
}

<table class="tb-zebra-rows">
	<thead>
		<tr class="header-odd" align="center">
			<th scope="col">Extension</th>
			<th scope="col">MIME type</th> 
		</tr>
	</thead>
	<tbody>
		<tr class="tablerowlight tr-even">
			<td>.3dm</td> 
			<td>x-world/x-3dmf</td>
		</tr> 
		<tr class="tablerowdark tr-odd"> 
			<td>.3dmf</td> 
			<td>x-world/x-3dmf</td>
		</tr> 
		<tr class="tablerowlight tr-even"> 
			<td>.a</td> 
			<td>application/octet-stream</td>
		</tr> 
		<tr class="tablerowdark tr-odd"> 
			<td>.aab</td> 
			<td>application/x-authorware-bin</td>
		</tr>
	</tbody>
</table>