How critical are macOS Mojave compatibility requirements? As per Apple support document, How to upgrade to macOS Mojave:


  1. Check compatibility
  
  You can upgrade to macOS Mojave from OS X Mountain Lion or later on
  any of the following Mac models. Your Mac also needs at least 2GB of
  memory and 12.5GB of available storage space, or up to 18.5GB of
  storage space when upgrading from OS X Yosemite or earlier.
  
  
  MacBook introduced in early 2015 or later
  MacBook Air introduced in mid 2012 or later
  MacBook Pro introduced in mid 2012 or later
  Mac mini introduced in late 2012 or later
  iMac introduced in late 2012 or later
  iMac Pro (all models)
  Mac Pro introduced in late 2013, plus mid-2010 or mid-2012 models with a recommended Metal-capable graphics card.
  


I am currently running macOS High Sierra on my Early 2011 MacBook Pro.

What does Apple's requirements mean for my ability to install Mojave? Is it possible or worthwhile to do so?
For an unpatched installer the requirements set forth are final. Early 2011 MacBook Pros are not supported and the installer will not work.

That does not mean that it does not work at all.

Using dosdude1's Mojave patcher you can install it easily, but with quite a number of some caveats:


  Current Issues
  
  
  Graphics anomalies: Currently, pre-metal video cards used in Mojave will produce a weird darkish grey Menu Bar and Finder sidebar when using the light theme. In the dark theme, these anomalies are not present, while other, less obvious anomalies are present (window corners may not render properly, bottom part of dock menus may have artifacts). A workaround for graphics anomalies in light mode is to enable Reduce Transparency in System Preferences > Accessibility > Display (this might create additional side effects beside the obvious loss of transpareny as some systems with pre-metal AMD graphics render the dock in dark gray).
  AMD Radeon HD 5xxx/6xxx series GPU acceleration: Currently, it is not possible to get full graphics acceleration when running Mojave on a system with a Radeon HD 5xxx or 6xxx series GPU. Mojave will be almost UNUSABLE without graphics acceleration. This includes the 15" and 17" MacBook Pro systems (MacBookPro8,2 and 8,3). If you want to enable GPU acceleration on these machines, you'll need to disable the AMD GPU (This will work on MacBook Pro 8,2 and 8,3 systems ONLY. You CANNOT disable the AMD GPU in an iMac.) Weird colors will also be produced when running Mojave with one of these video cards installed/enabled. To disable the AMD GPU on a 2011 MacBook Pro 8,2 or 8,3, follow the guide found here.
  


Concerning the last sentence: "To disable the AMD GPU on a 2011 MacBook Pro 8,2 or 8,3, follow the guide found here", I might add: and here ;)

Notice that disabling AMD on that machine also means losing the ability to drive a second monitor. Bad for multi-monitor setups, doing presentations… –– Also note that while the integrated Intel HD3000 will provide you with some GUI acceleration,  (but nothing like the Metal-API, as noted in Nimesh's answer) it is known to be a bit buggy, and increasingly hardware acceleration gets blacklisted by applications like Firefox, Chrome and VLC…

So, curiously: a defective discrete GPU makes a hacked Mojave install in these machines more attractive than a working one, as with a toasted dGPU you will lose less in the process.



Whether the upgrade is worth it for his machine is another issue. In a comment you wrote that 


  replaced the keyboard and the battery to get more life out of my MBP. I don't want to let go of my matt screen! And all my lovely ports!


This leaves it undetermined whether you upgraded from platter hard disk to SSD. The forced conversion to APFS renders this option undesirable on hard disks. On an SSD that might be not an issue, but I still don't like APFS and regard that filesystem as immature.

Then High Sierra and even Sierra are presumably still supported for some time regarding security updates or application compatibility. From that perspective there is no need to let go of that machine right now.

As this is totally unsupported by Apple: an early 2011 MBP might break at any time with a future update from Apple. Unless you really need a 10.14-only application –– or maybe die to get darkmode? – there is currently no compelling reason to do this if you want to work with that machine.

A final piece of opinion. If you love your machine with its matte screen, new battery, new keyboard and all those lovely ports: then experience tells me that any Mac lover is well advised to not upgrade immediately to an .0-OS-release from Apple. Do not upgrade now, wait a bit.



To accomodate the more general question title:

With a patched installer these are "the real" bare minimum requirements right now:


  Requirements:
  
  
  Early-2008 or newer Mac Pro, iMac, or MacBook Pro:
  MacPro3,1
  MacPro4,1
  iMac8,1
  iMac9,1
  iMac10,x
  iMac11,x (systems with AMD Radeon HD 5xxx and 6xxx series GPUs will be almost unusable when running Mojave. More details are located in the Known Issues section below.)
  iMac12,x (systems with AMD Radeon HD 5xxx and 6xxx series GPUs will be almost unusable when running Mojave. More details are located in the Known Issues section below.)
  MacBookPro4,1
  MacBookPro5,x
  MacBookPro6,x
  MacBookPro7,1
  MacBookPro8,x
  Late-2008 or newer MacBook Air or Aluminum Unibody MacBook:
  MacBookAir2,1
  MacBookAir3,x
  MacBookAir4,x
  MacBook5,1
  Early-2009 or newer Mac Mini or white MacBook:
  Macmini3,1
  Macmini4,1
  Macmini5,x
  MacBook5,2
  MacBook6,1
  MacBook7,1
  Early-2008 or newer Xserve:
  Xserve2,1
  Xserve3,1