I apologise if this is somewhat repetitive, as there are many questions like this but each person's situation is slightly different.
I am on the SOR and travel abroad about 5 times a year for both work and holiday.
When I travel to Europe, I routinely get stopped and asked questions on arrival in the foreign country. I assume this is because I have a Schengen Information System alert on me, presumably added when I notified the UK police of my foreign travel.
I have also travelled outside of Europe while on the SOR, to Canada, Mexico, Kenya and Thailand. I of course notified all these visits. For Canada I was economical with the truth on the eTA question about convictions, if you get my drift. In all 4 countries, I had absolutely no problem passing through border control. No questions at all - fill in a simple form on the plane or on a machine upon arrival, and they check/stamp your passport and wave you through quickly.
This surprised me, as the police obviously inform the Europeans about me travelling there, but not the other countries. So I guess they have used their discretion not to issue an Interpol green notice. Thailand might pop up as a suspicious place for an RSO, but it was for a friend's wedding in a rarely visited rural area, far from the infamous tourist areas etc.
The fact that they clearly don't bother to notify the non-European countries of my travel suggests that they have discretion regarding Interpol green notices, but no discretion for the SIS and are required to add any RSO who notifies travel to Europe. Is this correct?