> <xsl:apply-templates match="Records/Record/node()[name()='firstName']"/>

you presumably mean select not match (which is a syntax error) and it's
generally a bad idea (slower and not namespace-aware0 to text eleemnt
names using name() why not simply

<xsl:apply-templates select="Records/Record/firstName"/>

> and in most cases this would work, but of course this would conflict
> with any other customer info that also contained 'firstName' 

I can't guess what kind of conflict you see here, could you post a
slightly larger XML that also has elements that you wouldn't want to
select.

> Then do <xsl:apply-templates
> match="Records[template='customerProfile']/Record" />
again use of match here.

David

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