John Workman discusses this issue at length and gives several solutions in this discussion on his blog. Basically, parse the individual date components and recombine in whatever order you wish. For your case, a pure XSLT 1.0+ version would be:
<?xml version="1.0" encoding="utf-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:template match="date">
<!-- converts FROM <date>2001-12-31T12:00:00</date> TO some new format (DEFINED below) -->
<xsl:template name="FormatDate">
<xsl:param name="DateTime" />
<xsl:variable name="year" select="substring($DateTime,1,4)" />
<xsl:variable name="month-temp" select="substring-after($DateTime,'-')" />
<xsl:variable name="month" select="substring-before($month-temp,'-')" />
<xsl:variable name="day-temp" select="substring-after($month-temp,'-')" />
<xsl:variable name="day" select="substring($month-temp,1,2)" />
<xsl:variable name="time" select="substring-after($DateTime,'T')" />
<xsl:variable name="hh" select="substring($time,1,2)" />
<xsl:variable name="mm" select="substring($time,4,2)" />
<xsl:variable name="ss" select="substring($time,7,2)" />
<!-- EUROPEAN FORMAT -->
<xsl:value-of select="$day"/>
<xsl:value-of select="'.'"/> <!--18.-->
<xsl:value-of select="$month"/>
<xsl:value-of select="'.'"/> <!--18.03.-->
<xsl:value-of select="$year"/>
<xsl:value-of select="' '"/> <!--18.03.1976 -->
<xsl:value-of select="$hh"/>
<xsl:value-of select="':'"/> <!--18.03.1976 13: -->
<xsl:value-of select="$mm"/>
<xsl:value-of select="':'"/> <!--18.03.1976 13:24 -->
<xsl:value-of select="$ss"/> <!--18.03.1976 13:24:55 -->
<!-- END: EUROPEAN FORMAT -->
</xsl:template>
Another format (REPLACEs the EUROPEAN FORMAT section):
<!-- Long DATE FORMAT -->
<xsl:choose>
<xsl:when test="$month = '1' or $month= '01'">January</xsl:when>
<xsl:when test="$month = '2' or $month= '02'">February</xsl:when>
<xsl:when test="$month= '3' or $month= '03'">March</xsl:when>
<xsl:when test="$month= '4' or $month= '04'">April</xsl:when>
<xsl:when test="$month= '5' or $month= '05'">May</xsl:when>
<xsl:when test="$month= '6' or $month= '06'">June</xsl:when>
<xsl:when test="$month= '7' or $month= '07'">July</xsl:when>
<xsl:when test="$month= '8' or $month= '08'">August</xsl:when>
<xsl:when test="$month= '9' or $month= '09'">September</xsl:when>
<xsl:when test="$month= '10'">October</xsl:when>
<xsl:when test="$month= '11'">November</xsl:when>
<xsl:when test="$month= '12'">December</xsl:when>
</xsl:choose>
<xsl:value-of select="' '"/> <!--January -->
<xsl:value-of select="$day"/> <!--January 12 -->
<xsl:value-of select="','"/> <!--January 12,-->
<xsl:value-of select="' '"/> <!--January 12, -->
<xsl:value-of select="$year"/> <!--January 12, 2001-->
<!-- END: Long DATE FORMAT -->
You can recombine the elements in any way you choose.