Your issue is related to Mod Security rules of your Host. Your IP must be blacklisted. Check here: https://whatismyipaddress.com/blacklist-check
My IP is often listed and I have no clue why. Could be related to my ISP, but people all over the world have this issue.
I’m using CF7 on more than 300 websites and have been facing this issue for more than a year.
More info about the issue:
https://www.geminigeeks.com/bluehost-blocking-contact-form-7-submissions-409-conflict-error/
I request the plugin author to please fix the issue by simply renaming file/folder/any API paths, and make sure “contact” is replaced with “kontact” or something else. Bluehost refuses to do anything about the issue.