I created small tool called luster for downloading list of "likers" and "followers" of your Facebook page.
After download and unpack archive for your platform you can run it from terminal as
luster fans my-page-name
Where my-page-name is string identifier of your Facebook page.
You will be asked for email and password to your Facebook account. Note that this account need to have one of available page roles. Even Analyst is enough.
After while you should receive output similar to following
TIME,KIND,ID,NAME,LINK
1581665652,Like,111111111,John Doe,https://www.facebook.com/111111111
1581663355,Like,222222222,Kal Peterson,https://www.facebook.com/222222222
1581661970,Follow,333333333,Nikol Kus,https://www.facebook.com/333333333
This tool is based on reading table which can be found in Settings -> People and Other Pages section of your Facebook page.
Be aware that there is some limit up to 7k results from
Facebook side. I tested it on two pages with more than 20k of fans and
didn't get more then 7k results.
See https://github.com/zladovan/luster for details.