In Lore: It's complicated.
Firstly, there are smatterings of evidence here and there, and it's hard to pull together all the pieces, but none of the lore I've found proves that it would be impossible. Regardless, there is no reason you should constrain yourself to existing lore, rather than creating your own, even if it subverts your players expectations.
However, below are some lore-inspired reasons for Yuan-Ti to be capable of 'love', or other human emotions.
All quotes are from the Forgotten Realms Wiki, unless stated otherwise.
Firstly, from a lore perspective, in the forgotten realms at least Yuan-Ti originated as humans:
The yuan-ti were once human.1,2 [...] bred [...] by magically experimenting with and breeding men with snakes.
Simply put: Humans are capable of love, and you might argue so are some Yuan-Ti.
What is love? Baby don't hurt me
Yuan-Ti are communal, so they clearly understand the value of societies and relying on others rather than being purely solitary.
They also have the concept of 'friendliness', as per this FR Wiki excerpt:
Yuan-ti call themselves vrael olo (which means "favored ones"). Daily use typically uses the shortened "vrael", and can be modified to "auvrael" (meaning friendly or known yuan-ti) and "duthrael" (unfriendly or unfamiliar yuan-ti).3
Also, at least outside of FR Lore, the concept of love itself is nebulous at best, and even animals (as a counterexample to Yuan-Ti) are considered capable of emotion.
Even the fact that Yuan-Ti typically lay broods:
Female yuan-ti lay eggs in brood chambers, marking each clutch with its parentage, then abandoning them to the care of broodguards.
no source given in the wiki
Doesn't necessarily mean that they are not able to pair bond with one or more (as monogamy is not a requisite for love) individuals.
This behaviour seems all too similar to the rigid structure of Drow society, which has been comparatively expanded on much more than the Yuan-Ti. Despite that rigid structure though, and some people assuming all Drow are cold and heartless, there are examples of them experiencing emotions like love.
Though Pureblood and Malison are both described as 'wicked', 'arrogant' and 'self-centered'4, 5 that doesn't necessarily preclude feelings of genuine love (merely conflicted and complex emotions).
Despite being thoroughly wicked, the majority of purebloods had magnetic personalities. Like all yuan-ti, they tended to be arrogant and self-centered.
Like most yuan-ti, [malison] tended to be self-absorbed and arrogant.
Indeed, it's even hinted that they can have affections towards each other:
Prospective partners will coldly measure one another and if both agree that the match is promising, they usually mate, regardless of their personal affections towards each other.5
This seems to hint, that although they may be Cold of Heart, they merely look past their emotions to logical conclusions, not unlike Vulcans from Star Trek.
Exceptions that prove the rule
Just as Drizzt (and others) prove that not all Drow are evil, there are examples (though less clear cut) of Yuan-ti 'pair bonding' or 'becoming interested in other', either Yuan-ti or other species. All these are featured in the novel series 'Forgotten Realms: House of Serpents':
As you can see, the Yuan-Ti are a complicated bunch. Often portrayed as being cold, the above bits of lore should show it's not as simple as that.
Outside of Lore: It's your choice.
As others have argued, even if none of the above evidence existed, it's entirely your pierogi if you want to write or re-write lore, as per the 5e Monster Manual:
The alignment specified in a monster's stat block is the default. Feel free to depart from it and change a monster's alignment to suit the needs of your campaign. If you want a good-aligned green dragon or an evil storm giant, there's nothing stopping you.
Until Drizzt came along, we didn't have any examples of 'Good aligned Drow' (they probably existed in-universe though). And yet here we are now, with a more complicated and nuanced view of that race. The same logic can be applied to any species portrayed in D&D lore. Just because the authors of the lore have not 'put the head on the robot' so to speak, does not mean that the 'robot' can't be used for good, rather than doing harm by oversimplifying the portrayal of sentient creatures.
It's perfectly reasonable to say, these Yuan-Ti tend to be evil aligned due to societal/environment/magical factors, but outside of that, they are actually free to be any alignment.
In support of the above, there has also been an errata to Volo's guide to Monsters
Roleplaying a Yuan-ti (p. 98). The four paragraphs before the tables have been replaced with the following: “When you’re roleplaying a yuan-ti, the following
tables contain possible inspiration. They suggest characteristics that a yuan-ti might possess.”
Yuan-ti Pureblood Traits (p. 120). The Alignment trait has been removed.
This follows the general pattern of making humanoid creatures not restricted to a fixed alignment, or lore that limits them to a one-dimensional cultural expression.
References copied over from the Forgotten Realms wiki:
- David "Zeb" Cook et al. (1989). Monstrous Compendium Volume One. (TSR, Inc). ISBN 0-8803-8738-6.
- Gary Gygax (August 1983). Monster Manual II 1st edition. (TSR, Inc), p. 130. ISBN 0-88038-031-4.
- Ed Greenwood, Eric L. Boyd, Darrin Drader (July 2004). Serpent Kingdoms. (Wizards of the Coast), p. 10–11. ISBN 0-7869-3277-5.
- Reynolds, Forbeck, Jacobs, Boyd (March 2003). Races of Faerûn. (Wizards of the Coast), p. 151-152. ISBN 0-7869-2875-1.
- Skip Williams, Jonathan Tweet, Monte Cook (July 2003). Monster Manual v.3.5. (Wizards of the Coast), p. 262. ISBN 0-7869-2893-X.