Safety and reliability
In this context, "safety" refers to a products ability to function as advertised with no adverse affects to it nor the device in which it interfaces.
Is it safe to connect external screen to the MacBook via USB-C from the warranty perspective?
Why wouldn't it be safe?
The idea behind standardizing on USB is so that you can plug in 3rd party devices to expand and enhance the functionality of your computer. If plugging in devices voided your warranty, they wouldn't put the port there and instead we'd still have (our cherished) MagSafe power connectors.
If it wasn't safe to do something, the manufacturer wouldn't market that function as a feature of the product.
Since power is supplied to MacBook there is a (small) risk to damage the laptop.
Technically speaking, anything you plug into your laptop has the potential of damaging it.
Since USB 1.0, power has always been supplied - 5V @ 500mA. It is only since the USB Power Delivery Specification was implemented that more power can be delivered; up to 100W or 20V @ 5A.
This is why you should always stick to known brands and avoid the cheap knockoffs.1 It's a timeless adage - you get what you pay for - but it still holds true today. That said, it still doesn't rule out the possibility of a manufacturer defects. While very rare, they do happen; your expensive Dell or LG could potentially damage your MacBook.
Technically, we're plugging in a non-standard power adapter; can it void the warranty?
If you are plugging in a display that provides power and conforms to the USB PD specification, especially if it's USB-IF certified it's not "non-standard." That device is designed to connect, interface with, negotiate, and accept power. You plugging in this device, does not void your warranty.
Apple decided to go from a (beloved) proprietary power connector - the MagSafe - to a widely adopted industry standard connector that literally has "universal" in the name: USB-C. Simply using a different charger doesn't void your warranty. If damages arise because it was defective, that's a different story.
Is the Macbook 12 inch's USB-C charger interchangeable with other USB-C chargers or devices?
From a pragmatic point of view using your Dell or LG monitors as the basis of your postulate, how can you possibly have a "genuine Apple" charger coming out of a third party monitor? This would mean that the moment you connect a non-Apple monitor you void the warranty. Until recently, Apple had exited the display business when they ceased production of the Thunderbolt Display in June of 2016.3 The display provided charging via a MagSafe connector; the Thunderbolt port didn't supply power. Therefore, it would be virtually impossible to "officially" charge a later model MacBook with this display.
Do screen manufacturers such as Dell or LG have any agreement with Apple?
Speaking as someone who worked in product management for a hardware manufacturer (in a past life), there are no agreements between companies that spell out any sort of liability assignment or otherwise with respect to each other's hardware. From a practicality standpoint, this would be absurd - think about how many display vendors there are. That alone would be next to impossible to manage. Now, expand that to all the different USB devices and accessories. There's no way to manage warranty reciprocity agreements to that scale thus making it totally unfeasible.
From the perspective of the manufacturer, the warranty generally covers the products fitness or in other words, it's ability to do what it says it will do. If you read the fine print, there will always be a clause exempting coverage for misuse/abuse.
From Apple's own warranty language, they basically say this:
This Warranty does not apply to any non-Apple branded hardware products or any software, even if packaged or sold with Apple hardware. Manufacturers, suppliers, or publishers, other than Apple, may provide their own warranties to you – please contact them for further information. 2
What Voids Your Warranty
In short, misuse, abuse, and anything that's covered in the warranty language. Ultimately, it comes down to what you can prove. Here's a short excerpt from the hardware warranty; I encourage you to review the whole section at the link provided.
Software distributed by Apple with or without the Apple brand (including, but not limited to system software) is not covered by this Warranty. ... Apple does not warrant that the operation of the Apple Product will be uninterrupted or error-free. Apple is not responsible for damage arising from failure to follow instructions relating to the Apple Product’s use. 2
Can Apple Void Your Warranty Solely for Using a Third Party Accessory?
No. The Magnuson-Moss Warranty Act4 (in the US, your country's laws may differ) gives protection to consumers in that installation or use of third party accessories cannot void the warranty unless they it can be proven that the part or accessory in question is the reason for the failure.
The FTC (Federal Trade Commission) specifically addresses this in warning letters sent to several companies5:
...companies can’t void a consumer’s warranty or deny warranty coverage solely because the consumer uses a part made by someone else or gets someone not authorized by the company to perform service on the product.
(Hover for Opinion)
This means that warranty void stickers6 and using your Dell monitor that conveniently supplies power to your MacBook Pro for charging cannot void your warranty. Period.
I am not a lawyer; more importantly I'm not YOUR lawyer. I don't play one on or for any content provider. While many references have been made to legislation as well as agency opinion in this answer, my opinions are my own and should not be construed as legal advice. Seek out your own lawyer if you have a specific and/or real world question.
1 Cheap USB-C Cables Could Kill Your Phone or Laptop; Gizmodo, Feb. 2016.
2 Apple One Year Limited Warranty- US ; https://www.apple.com/legal/warranty/products/embedded-mac-warranty-us.html
3 Wikipedia: Apple Thunderbolt Display
4 US Code - Title 15, Chapter 50, Sections 2301-2312
5 FTC staff sends warranty warnings; Federal Trade Commission Business Blog; Fair, Leslie; April 10, 2018.
6 FTC: Ignore That Sticker Saying Your Warranty Will Be Voided; Laptop Mag; April 11, 2018