Quick test of APNG supporting browsers (current Safari and Firefox).  Navigate to request.urih.com, which reports the client request headers.  Results:

Chrome 59
Host : request.urih.com
User-agent : Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/59.0.3047.4 Safari/537.36
Accept : text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,image/apng,*/*;q=0.8
Accept-encoding : gzip, deflate, sdch
Accept-language : en-US,en;q=0.8
Upgrade-insecure-requests : 1
Connection : keep-alive

Firefox 52.0
Host : request.urih.com
User-agent : Mozilla/5.0 (Windows NT 10.0; WOW64; rv:52.0) Gecko/20100101 Firefox/52.0
Accept : text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-language : en-US,en;q=0.5
Accept-encoding : gzip, deflate
Upgrade-insecure-requests : 1
Connection : keep-alive

Safari 10.0.3
Host : request.urih.com
Accept : text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
User-agent : Mozilla/5.0 (Macintosh; Intel Mac OS X 10_12_3) AppleWebKit/602.4.8 (KHTML, like Gecko) Version/10.0.3 Safari/602.4.8
Accept-language : en-us
Accept-encoding : gzip, deflate
Upgrade-insecure-requests : 1
Connection : keep-alive

Seems that only Chrome adds image/apng to the Accept header. Firefox and Safari support APNG, but do not add it to their Accept.

The question then network / loader peeps: why does Chrome need to change the Accept header when other browsers do not?  Could it cause compat problems?

Answer: sent in chrome so that devs could decide on the server-side about what to serve and not need to sniff.