The answer to your question is No, using versatile weapons with two hands does not disqualify them as monk weapons.
But not because of any reason that made you ask the question, because your whole question is wrong as it's clear from your question you haven't understood the paragraph in question.
The paragraph in question on pg. 78, PHB says (emphasis mine):
At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
Let's look at what that paragraph really says.
The first thing it does is stating that at 1st level a monk has a master of different combat styles using unarmed strikes and monk weapons.
The second thing it does is stating that monk weapons are shortswords and any simple melee weapon that doesn't have either the heavy property or the two-handed property.
That's everything that paragraph states. It simply tells you that monks fight unarmed or with monk weapons and then defines monk weapons as either shortswords or any simple melee weapon that isn't heavy or requires two-hands to use.
Simple melee weapon with heavy or two-handed property = not monk weapons.
Simple melee weapon without heavy or two-handed property = monk weapons.
So what about the versatile property? A weapon with that property just gives you the option to use two hands during an attack for greater damage.
However, in this case whether a weapon has the versatile property or not has no impact on the RAW as it only purpose in this case is to define what a monk weapon is, which is a shortsword or any simple melee weapon without either the heavy property or the two-handed property. Any other properties such as light, finesse, reach or versatile has in this case no bearing on the rules. Nor does how you use said weapon.
No
Every class proficient with martial weapons is also proficient with simple weapons, so there would be no mechanical advantage to using a trident over a spear (unless in some unforeseen circumstance you needed the extra 1lb).1
There would be a reason to use a spear (simple weapon) and not a trident (martial weapon), but not the other way around. Bards, clerics, druids, monks, rogues, and warlocks are proficient with simple weapons but not martial weapons. For them, their proficiency bonus would be an advantage of the spear over the trident.
However, these are not the only weapons with the same mechanics (other than price and weight). The following martial weapons are mechanically identical:
- battleaxes and longswords are both versatile weapons causing 1d8 (1d10 two-handed) slashing damage
- morningstars and war picks both cause 1d8 piercing damage
- The "Variant Entertainer: Gladiator" background (PHB, p. 131) allows a player to "replace the musical instrument in your equipment package with an inexpensive but unusual weapon, such as a trident or net." RAW this only gives the trident as equipment. However, a DM could house rule that it also grants proficiency (in place of the music instrument from the Entertainer background). If allowed and taken by a sorcerer or wizard, they would have proficiency with tridents but not simple weapons (i.e, spears).
Best Answer
The cambion's spear attack does fire damage, but no rule says that the spear itself retains that property.
A statblock only defines what a creature's attacks do, not the game statistics of any items they may carry. In this case, the cambion may make a spear attack dealing 1d6+4 damage plus 1d6 fire damage, but there is no rule or descriptive text which would define that the spear retains that property.
The ethos of D&D 5th edition is that a rule says what it says and no more.1 Therefore, the rules say only that the cambion deals extra fire damage with his spear attack, not that the spear itself deals that damage in anyone else's hands.
It's also not common (perhaps unprecedented)2 for a creatures in D&D 5th edition to have a specific magic item in their statblock. Treasure from encounters is handled under its own rules in the Dungeon Master's Guide.
Lore-wise, the cambion has many supernatural abilities, specifically including the ability to create and throw fire, so it's very easy to imagine that fire surrounds any weapon he wields; conversely, flaming weapons are quite rare and difficult to acquire3, so many would not have this specific item.
Of course, the DM's word is law, so you could as DM say that cambions do indeed carry actual magic flaming spears, but only if you want your player characters running around with a load of flaming spears after they defeat an army of cambions. For that reason, I don't recommend it.
1 This is a design principle put forward by D&D 5e core designer Jeremy Crawford, and is widely used as a guideline for DMs adjudicating ambiguous rules. For example, in How much fire damage does igniting Grease deal?, Crawford's interpretation is that Grease isn't flammable because the rules do not say that it is. This attitude contrasts with D&D 3.5 where the DM was specifically advised to interpret ambigious rules by inference from other similar rules.
2 The only instance I'm aware of where a monster is described as having a magic item is the flind in Volo's Guide to Monsters, whose descriptive text says "It wields a flail imbued with powerful magic by Yeenoghu himself". However, even in this case, the statblock does not describe the weapon itself, only the attacks which the flind can make. It does not specify what happens if a PC tries to wield the flail, nor even is it made explicit whether the flail is a magic item, or merely temporarily imbued as a warlock may imbue his pact blade. If a DM ruled that a PC gains all the flail attacks the flind had, that PC now has a weapon dealing 4d10 bonus psychic damage, which is exceptionally powerful for an item you might gain around level 9, and I do not believe this was the designer's intent.
3 According to the item guidelines, magic items are only found in hoards, rather than standard per-monster treasure. The guidelines suggest that the PCs will in total acquire around 18 rolls on the CR 5–10 table, or 3 hoards per level, and 80% of these hoards will not even reach level Table F, the first table to give a +1 weapon. A cambion could have a magic weapon, but most won't.