Openwrt never used apache. The historical "White Russian" versions of openwrt (all those released before spring 2007) included a web interface that was implemented in shell script. Frankly, I would be surprised if the thing had no security issues.
However, modern "Kamikaze" releases of openwrt have no web interface at all; you configure them by ssh'ing in and editing config files, just like on a normal Linux server.
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