Joannalannister recommended that I ask you: How insulting would it be if someone broke off negotiations for a betrothal in order to have another one arranged? Like, it’s really obvious that Family X broke off negotiations with Family Y to immediately begin negotiating with Family Z.

Good question!

There’s a couple factors involved. 

First, how far along were the negotiations? If they were still in the preliminary stages, I think there’s a common understanding that everyone’s out there in the marriage market trying to make the best deal for their kid, so no hard feelings. However, if they were about to read the bans and suddenly someone jumps ship, there would be a lot of harmed feelings. 

Second, what are the relative power and prestige of the three houses? As we see with the (admittedly extreme) case of the Freys, the Starks, and the Westerlings, a big part of the Freys’ grievance was that they were ditched for a much poorer and weaker house, but one with a more prestigous bloodline, hitting the Freys right in the sore spot. But while the Freys would no doubt be angry regardless, if Robb had married Margaery Tyrell, it would be much harder to kick up a public fuss about that. 

Third, what are the previous relations between the various houses? In cases like the Brackens and the Blackwoods where two houses have a notable feud, any spat where one house gains at the the others’ expense is going to be viewed as personal, not business. (Think about how the Brackens and Blackwoods felt about Aegon IV’s mistresses, and then instensify it because you’re talking about more formal unions). 

Fourth, how public and/or harsh is the break? Tywin and the Unnamed Dornish Princess’ conflict over marriage proposals between the Lannisters, Martells, and Targaryens got very ugly, escalating into open blood feud, in no small part because there was very little diplomacy in the way that people were turned down, so that the loss of a marriage alliance was compounded by a loss of public face.