Privacy changes, scraping and general "aggressive" signup flows to Facebook have caused sharing public photos to be a slightly annoying process however it's still possible.
As long as the album is "Public" non-Facebook users will see it.
Yes, you will still see the dialog asking a user to sign up you can call it aggressive signup flows or whatever you want, as long as you close that you will see the album.
Click "Not Now"
So the link to an album with Public setting looks like
Where ALBUM_ID is the ID of the album you want to share.
To get to this easy, you can choose clicking share (at the bottom where like, comment and share are shown) then choose "Share in a Private Message" to get a way to copy the link.
And then copy the link
There are no other options as far as I know, maybe embedding the photos but website style development questions are out of scope here.
The share by email option no longer works (it was removed)
I know it's not like the options offered in the past but that's just how it is now.