HTML tags are stripped out while indexing Rich Text field content OOTB in Sitecore and this is a good practice in general as well. But Yes you can configure this, there are two ways to index any RTE field with html tags, first for a single field and, second for all the RTE fields.
Single Field- Create a patch config for SITECORE FIELDTYPE MAP
section, this map a field type by name to a Strongly Typed Implementation of the field type e.g. html maps to HTMLField. Will add below section under <fieldReaders
section. It will have the fieldReaderType
= Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch
<mapFieldByFieldName hint="raw:AddFieldReaderByFieldName">
<fieldReaderfieldName="RTEFieldName"fieldReaderType="Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch" />
</mapFieldByFieldName>
Final output in your showconfig would be like -
<fieldReaders type="Sitecore.ContentSearch.FieldReaders.FieldReaderMap, Sitecore.ContentSearch">
<param desc="id">defaultFieldReaderMap</param>
<mapFieldByFieldName hint="raw:AddFieldReaderByFieldName">
<fieldReaderfieldName="RTEFieldName"fieldReaderType="Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch" />
</mapFieldByFieldName>
<mapFieldByTypeName hint="raw:AddFieldReaderByFieldTypeName">
<fieldReader fieldTypeName="checkbox" fieldReaderType="Sitecore.ContentSearch.FieldReaders.CheckboxFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="date|datetime" fieldReaderType="Sitecore.ContentSearch.FieldReaders.DateFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="image" fieldReaderType="Sitecore.ContentSearch.FieldReaders.ImageFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="single-line text|multi-line text|text|memo" fieldReaderType="Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="integer" fieldReaderType="Sitecore.ContentSearch.FieldReaders.NumericFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="number" fieldReaderType="Sitecore.ContentSearch.FieldReaders.PrecisionNumericFieldReader, Sitecore.ContentSearch"/>
fieldReaderType="Sitecore.ContentSearch.FieldReaders.RichTextFieldReader, Sitecore.ContentSearch" />
<fieldReader fieldTypeName="multilist with search|treelist with search" fieldReaderType="Sitecore.ContentSearch.FieldReaders.DelimitedListFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="checklist|multilist|treelist|treelistex|tree list" fieldReaderType="Sitecore.ContentSearch.FieldReaders.MultiListFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="icon|droplist|grouped droplist" fieldReaderType="Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="name lookup value list|name value list" fieldReaderType="Sitecore.ContentSearch.FieldReaders.NameValueListFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="droplink|droptree|grouped droplink|tree|reference" fieldReaderType="Sitecore.ContentSearch.FieldReaders.LookupFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="attachment|frame|rules|tracking|thumbnail" fieldReaderType="Sitecore.ContentSearch.FieldReaders.NullFieldReader, Sitecore.ContentSearch"/>
<fieldReader fieldTypeName="file|security|server file|template field source|link" fieldReaderType="Sitecore.ContentSearch.FieldReaders.NullFieldReader, Sitecore.ContentSearch"/>
</mapFieldByTypeName>
</fieldReaders>
RTE Field Type - For all the RTE field type you just need to change the fieldReaderType of “html|rich text”
fieldReader to Sitecore.ContentSearch.FieldReaders.DefaultFieldReader
. recommanded practice to create patch for config update.
<fieldReader fieldTypeName="html|rich text" fieldReaderType="Sitecore.ContentSearch.FieldReaders.DefaultFieldReader, Sitecore.ContentSearch"/>
After updating these config chagnes you need to do reindexing.