Is there an email header that will avoid responses from most auto-responders?
Solution 1:
Adding a "List-Id" header or a "Precedence: list" header should solve the problem for well behaved auto-responders. The behavior comes from the original vacation program for UNIX. Among other things it will not respond to an email that appears to come from a list. You would probably be better off with the List-Id header line than taking chances with the precedence setting but try both.
Solution 2:
I believe Precedence: Bulk is the canonical setting, but the number of people whose autoresponders obey it is miniscule. Fact is, the vast majority of autoresponders are badly behaved.
Solution 3:
No, there nothing that always works.
There's standards
sending wuth a null return path (empty envelope sender, SMTP MAIL FROM:<>)
should prevent autotoresponders (https://tools.ietf.org/html/rfc5321#section-4.5.5)
Implementers of automated email processors should be careful to make sure that the various kinds of messages with a null reverse-path are handled correctly. In particular, such systems SHOULD NOT reply to messages with a null reverse-path,
setting an Auto-Submitted header should also work (https://tools.ietf.org/html/rfc3834#section-2)
Automatic responses SHOULD NOT be issued in response to any message which contains an Auto-Submitted header field
And then there's Microsoft...
section 2.2.3.2.14 in https://docs.microsoft.com/en-us/openspecs/exchange_server_protocols/ms-oxcmail/e489ffaf-19ed-4285-96d9-c31c42cab17f (URL subject to expire at Microsoft's whim)[MSOXCMAIL] 2.2.3.2.14
says
2.2.3.2.14 Suppression of Automatic Replies
To set the value of the PidTagAutoResponseSuppress property (section 2.1.3.2.20) to -1, indicating that all automatic replies to the message are to be suppressed, clients SHOULD write an X-Auto-Response-Suppress header with the value "All".
...
MIME readers SHOULD<116> map individual elements of an X-Auto-Response-Suppress header to bits in the value of the PidTagAutoResponseSuppress property according to the table. If both the X-Auto-ResponseSuppress and Precedence headers are present, the PidTagAutoResponseSuppress property value SHOULD be 0xFFFFFFFF but MAY<117> be 0x00000000. If the value of the X-Auto-Response-Suppress header is other than as specified in the table in section 2.1.3.2.20, MIME readers SHOULD<118> ignore the entire header.
Those little notes are most revealing
<116> Section 2.2.3.2.14: Outlook 2010, Outlook 2013, Outlook 2016, and Outlook 2019 do not read the X-Auto-Response-Suppress header.
<117> Section 2.2.3.2.14: Exchange 2003 uses this value for the PidTagAutoResponseSuppress property ([MS-OXOMSG] section 2.2.1.77).
<118> Section 2.2.3.2.14: Exchange 2003, Office Outlook 2003, and Office Outlook 2007 ignore the X-Auto-Response-Suppress and Precedence headers.
so presubamly Exchange Server 2007 or newer want X-Auto-Response-Suppress
and Outlook wants Precedence
Note that this is ignoring https://tools.ietf.org/html/rfc3834#section-2
(Because Precedence is not a standard header field, and its use and interpretation vary widely in the wild, no particular responder behavior in the presence of Precedence is recommended by this specification.)
The best move is probably to do all four, or as many of these as are possible.