I change my location quite frequently and every now and then Facebook prompts me to confirm the location by tagging friends’ pictures.
Are there any means to avoid these prompts, other than staying in the same place?
You can turn off Login Notifications/Approvals. It’s in Account Settings → Security.
It happens whenever Facebook detects 'uncommon' activity/'suspicious' activity such as logging in from a IP address located far away from the regular one.
What you can do is, log into Facebook from your own country - with the "Keep me Logged in" feature on your laptop or mobile, then travel to the other country and just open your already logged in Facebook account.
Also, if you log in from a mobile app or a mobile device, or from m.facebook.com from any Laptop/Computer, this kind of security check will not occur. - After getting logged in by this way, you can head to www.facebook.com and use the complete site.