I see this has not been answered properly yet, and not sure if you still need it but it is the field UserPreferencesHides1BrowserUI on the User object. Thing to note is that the boolean value is opposite to what you think. If the value is True, then the check box is unchecked and vise versa.
The documentation does say that there's a limit.
User passwords cannot exceed 16,000 bytes.
The answer does not say that the maximum maximum is 1,333 characters, but rather the minimum maximum is 1,333 characters. The maximum is 16,000 characters if you use only UTF code points 0x01-0x7F, which mirror the same 127 code points in LATIN-1/ISO-8859-1 for ...
To migrate users from one organization to another, you can user Dataloader, SFDX or other tools.
I would suggest to extract users from one org using Dataloader.
Then modify username (append some random text to end of the username, for
example modify email@example.com to firstname.lastname@example.org)
You might need to fix the Profile links and UserRole links as well.
Then upload the ...
Did you check if the Organization-Wide Defaults for User is set to 'Private' in the org that has this issue?
If it is, change it to 'Public Read Only' so that a user can see other users.
Note: I am only writing my comments/suggestions as an Answer as I don't have enough reputation to comment on the question.
As manjit5190 pointed out in the comments, profiles don't control what records people see; they control what kinds of records they can see.
For example, say a business has two profiles that can see opportunities -- Sales and Support. Sales needs access to opportunities so that they can generate new revenue, and support needs access to submit replacement ...