ls /etc/selinux/
restorecond.conf  semanage.conf
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Without doing further research myself, I can't really comment on those files... What do they contain?  At least, the fact that there is a /etc/selinux/ directory indicates that the issue might not be totally irrelevant...

man apachectl shows no -X or -p options.

Sorry if I wasn't being clear. -X is an option of the actual binary (i.e. httpd or apache, depending on distro), and the -p option belongs to strace.

You could either simply start httpd manually (after having terminated the running instances with apachectl as usual), or edit the -X into the apachectl script (in the "start" section¹). If you do start it manually, it's probably a good idea to first check with which options it is being run currently (ps axf, or some such), and use those in addition to -X. Also, I forgot to mention that with strace you probably also want the option -f.

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¹ something like:

...
start|stop|restart|graceful)                             
    $HTTPD -X ...
            ^ insert this
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