By the way, if you click the invitations button from the admin screen, it will show the list of id's for participant 1, 2 and 3 and invite participants 1 and 3 and skip participant 2 as expected

Is it possible for you to give us a pull request with the fix?

Sorry, I wouldn't really feel comfortable doing that. I'm not at all familiar with the code base (or even with PHP for that matter).

Moving this to a Feature Request.
The stopping is behaving as expected:

https://api.limesurvey.org/classes/remotecontrol_handle.html#method_invite_participants

Returns array of results of sending. The sending stops on the first error (ie. when a token is invalid).

Well, I will give you that it is as documented (which I missed, I must admit, although we implemented our API ) :) I still think it's a bit odd that the same functionality of 'don't select any participants in particular and just invite all participants that are valid' from the admin panel works as I expect it to, but the remote control API has different rules. It seems like there's no way for me to emulate with RemoteControl, what I can do in the admin panel. Am I missing something here?

Of course i would then expect the same for remind_participants, but I didn't check if that behaves the same way.

As discussed with @c_schmitz will be working on this.
Should add a new parameter: continueOnError = false

remind_participants should be updated as well.

PR: https://github.com/LimeSurvey/LimeSurvey/pull/2866

Marking it as tested as it has the automatic test

Fix committed to master branch: http://bugs.limesurvey.org/plugin.php?page=Source/view&id=34240

Fixed in Release 5.6.3+230130