The find familiar spell summons a spirit in the form of a creature not the creature itself. So a pseudodragon summoned by the spell is not a normal pseudodragon, you could recast the spell and reshape the familiar into a raven or imp and it would be at it's core the same entity.
Try to compare it to other pact boons. Blade pact gives you a melee weapon, which is considered magical, and you get proficiency in it. Tome pact gets you three cantrips. Both of those benefits are nice, but nowhere close to magic resistance. Chain pact basically gets you a slightly improved 1st-level spell (find familiar). That (IMO) is exactly in line with other boons.
In short, magic resistance won't break the game, but it far outweighs other benefits gained at lower levels.
Regards.
The problem with familiar-granted magic resistance is that you have to have your familiar within 10 feet, and the familiars in question have 7-10 hit points and poor saves. The first time you use that magic resistance against an area attack, you're apt to lose it.
I do think it's intended that you should get the resistance; remember that the Monster Manual was released after the PHB. Because the sidebars just happened to all be on monsters that warlocks can get as familiars, I suspect the sidebars were a kind of stealth errata to beef up the Pact of the Chain.
The exact wording, from page 108 of the PHB: When you gain this feature, choose three cantrips from any class's spell list.
The problem with familiar-granted magic resistance is that you have to have your familiar within 10 feet, and the familiars in question have 7-10 hit points and poor saves. The first time you use that magic resistance against an area attack, you're apt to lose it. Better make sure you've got plenty of find familiar components on hand. (The incense is less of a problem than the need to tote around a brass brazier and spend 1 hour re-casting the spell.)
I do think it's intended that you should get the resistance; remember that the Monster Manual was released after the PHB. Because the sidebars just happened to all be on monsters that warlocks can get as familiars, I suspect the sidebars were a kind of stealth errata to beef up the Pact of the Chain.
Warlock's pact boons doesn't end when you get them, we also have consider how the pacts scale thru levels so we have to consider the available warlock invocations.
Among the three, the Chain pact is the pact with the least useful invocations to upgrade it thru higher levels. Leaving you with just an optional invisible familiar that will never improve its statistics or abilities. Easily the Blade and Book have it better thru levels.
Besides the fact that the magic resistance of these familiars as stated in MM (IMHO), it may seem its a bit advantageous at the first few levels, but chain related invocations or familiars of warlocks will not scale or improve thru levels compared to Blade and Tome. It makes sense why these options were presented in MM.
To put the other perspective and by the strict letters of the sentence, I agree with your DM and other player. I'm not sure whether they thought about this in detail enough when writing it so can't be sure of the actual intent but the "list" is singular rather than plural and why bother specifying "cantrip from spell list" when it would be simpler to write "any cantrip" if that was the intention.
Yeah. Unfortunately, I agree.It is not ambiguous. It is not open for interpretation. If multiple classes were intended, it would have been written as such.
The find familiar spell summons a spirit in the form of a creature not the creature itself. So a pseudodragon summoned by the spell is not a normal pseudodragon, you could recast the spell and reshape the familiar into a raven or imp and it would be at it's core the same entity.
So I would say that unless you get a real imp, quasit, or pseudodragon to bond with you the sidebar abilities like shared magic resistance wouldn't apply.
This is true, and it's part of the reason that the form of the creature to be used is the one in the back of the PHB, and not the one in the MM sidebar.So we are interpreting this as whenever you call a familiar (by ritual), you can choose any form you wish that time. Not choose one form and stick with it forever. You can even choose depending on your need that time or adventure.
MM sidebar (again, IMO) is there to let the DM use it for NPCs, or as a special reward for a spell caster PC (including clerics, druids, eldritch knights, arcane tricksters, etc.)
As to the cantrip question, "from any class's spell list" translates to me to allow a choice from multiple and all class lists.
Yes. -- the wording is designed to avoid confusion, and we are making things unclear without need.If they had written "any cantrip", then it would be still any within the context of being limited to the Warlock's list.
-- a fuller answer is below, but what is written is correct, and it should be singular (warning: grammar ahead).In the phrase, "...any class's spell list", the word 'class' is singular.
The plural possessive of class, "belonging to more than one class", is classes' . The phrase is "any [singular] class's", not "any [plural] classes'..."
It is not ambiguous. It is not open for interpretation. If multiple classes were intended, it would have been written as such.
EDIT TO FURTHER NOTE: AND it would say "spell lists" [plural], not "list" [singular].

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.