I assume you want your site moderator and site admin can able to send conversation message to everyone on the site right?

If that is the case, I would suggest you create a new profile type for your site moderator and site admin then enable this "Allow Moderator Access" from the profile type configuration setting, then only these profile type users can able to send conversation message to all the registered user.

I mean normal users how can send message to any one when "Allow Messaging Non Friends" id turn off?
the privacy field for receive message is not match with backend !!

For the normal registered user can't send message to non-friend user if this setting turn off "Allow Messaging Non Friends".

The system will take a look this setting "Allow Messaging Non Friends" first then only user privacy.

If you would like to enabled this setting "Allow Messaging Non Friends" but you would like to restrict some of the user can't be send message to other (e.g. user A), user A have to set his privacy who can message me to "my friends" (screenshot : https://monosnap.com/file/ExrOomxLFBJKEYsLbWYmEnALny6ilT )

please look my attachments pgoto

first i turn off "Allow Messaging Non Friends".
then user active privacy who can message me to "all members"
so non friends can't send message to me

you can test in my website and see all settings

It is correct behavior in Easysocial.

If turn off this setting Allow Messaging Non Friends which mean that whoever not friend with you, they can't send message to you even through your privacy set to allow this "Star members".

Unfortunately it is no other way to other your site member can send conversation message to one of the specific member on the site.

no problem but when we turn on Allow Messaging Non Friends , all members are in list of converskit .
plz fix this problem and make flexible ACL for members
thank you for design best Social. i love easysocial and stay with you to end

Actually this is not a problem, it just that different website have their own different requirement, perhaps you can request this feature into our voice page here https://stackideas.com/voices/easysocial so everyone else on the site could vote for it as well.

The team will usually prioritize features that are in popular demand during the development process of the next major release.

By the way, thanks for loving Easysocial product