Without knowing the details of the exact case behind the restraining order, it's hard to be certain the bar is set "far too low" as you assert. Set a hard bar like that, and many will simply see "I can get away with that!", and find as many such bars they can scrape under as possible - making up in volume what they lack in direct effect - or a line to slowly cross further and further when not nipped in the bud. This is, ultimately, why intent matters.
Sufficiently strong-willed people can ignore death threats as "inconsequential, empty bluster." However, this is neither necessarily wise, recommended, or easy, nor does it disqualify such threats as harassment.
While an invite is no death threat, I'd note there's another bar in play here too: The former girlfriend was, if we're to give her the benefit of the doubt, perturbed enough by this invitation to go down to the police station.
Sufficiently strong-willed people can ignore death threats as "inconsequential, empty bluster." However, this is neither necessarily wise, recommended, or easy, nor does it disqualify such threats as harassment.
While an invite is no death threat, I'd note there's another bar in play here too: The former girlfriend was, if we're to give her the benefit of the doubt, perturbed enough by this invitation to go down to the police station.