How do I remove or disable the Photos app in El Capitan?
UPDATE: I have unselected my answer because an icon-less and half-working (see screenshot) version of Photos.app appeared on my system and opened automatically on SD-card insert.  This worked and did not cause problems for months, and now Photos is back 

El Capitan has a new feature called System Integrity Protection. It does not allow the deletion of preinstalled apps.  This link gives details for disabling it.  The short of it is:

Restart and hold Command+R to go into recovery mode.  Open "Terminal", found in the "Utilities menu" and use the commands

$ csrutil disable; reboot


to disable SIP and reboot.  Now open Terminal.app normally and do

$ cd /Applications/
$ sudo rm -Rf Photos.app


and live happily ever after.

A few caveats: I don't know what SIP does specifically, but this post suggests you should at least re-enable it right away (and perhaps not disable it at all, ever).  Go ahead and do that by using the command 

$ csrutil enable; reboot


in Recovery mode (see above).  I also don't know whether El Capitan has Photos.app-dependent system processes or not, so your mac may potentially not work the way you want it after this.  I have protected myself by first Archiving Photos.app and leaving Photos.app.zip in /Applications/, but again, I don't even know if this is good enough.  So proceed at your own peril!

Finally, this will work to get rid of any bundled system app (but the same or more severe warnings apply).