I dunno but I assume not after the number of times I've emailed MPs telling them to kill themselves.
See this is what I want to get a read on, because they're also having cops visit people over inane comments. Are you using name and return address lmao?
Yeah, full contact details in the signature. They never reply, the cowards.
To give a more helpful answer to your question, I suspect the distinction comes in volume, disruption, and actionability - my emails are nothings, just some random citizen venting anger. If I were sending huge volumes to a specific MP rather than one every few months to the villain of the week, they'd probably come down on me for harassment. If I was a known extremist actor like some of the people I organise with (all ALF) or included details indicating I had an actionable plan to harm them, they'd probably treat it as a serious threat.
On the other hand, my parents were communist organisers during the second half of the cold war, so they get cops turning up at the door if they even hint at planning a protest or demonstration on social media.
My mindset is when you get a physical movement or very large messaging campaign or online organization going that's inevitably the point you will encounter law enforcement in some form. So this tracks. Probably a lot of people on the old man yells at cloud list no offense. Ideally everyone in the entire country could pen a furious letter daily.