Let's go through all of this.
But they are basically talking about the vulnerabilities of the vPro technology, specifically the AMT bug (sorry I can't link more here, search for CVE-2017-5689), where a lot of people have panicked to disable the AMT system due to the massive bug that has been discovered earlier this year
You likely don't have AMT as this is usually only available on Xeon architecture chips, but there have been reports that it might be exploitable on some desktop architectures too. Disabling it is possible, see this thread on Intel's forums for details. If your system doesn't offer this option in the UEFI/BIOS, you'll either need a custom one (see later in this answer) or you'll need to clean your IME firmware to remove the functionality entirely (also discussed later).
Anti-Theft Technology, which can basically lock your computer, even via remote access (huge security vulnerability)
Sort of. You need to register your device with a provider (e.g. Intel, McAffee, or your organisation's administrators) in order to make it functional. At this point the provider can then lock the BIOS remotely if you report it stolen. The thread linked above also explains how to turn this off, but the enable/disable toggle is easily found in most UEFI/BIOS menus.
Execute Disable Bit, I am not sure what this does, but it sounds kind of invasive
Don't be scared by things you don't understand! Be curious. Execute Disable Bit is a really important security feature - it's the hardware feature that underpins No-Execute (NX), otherwise known as Data Execution Prevention (DEP) on Windows.
Identity Protection Technology, sounds like a huge privacy invasion
Nope. IPT is designed for use in enterprise environments where you want hardware-supported 2FA or PKI integration. It doesn't do anything unless you configure and enrol it.
Intel VT-x, which creates a subsystem that does have full privileges, but allegedly doesn't have access to the main system
I don't know where you've read this, but it's nonsense. VT-x is hardware virtualisation support. It includes special instructions which help speed up the process of virtualising a secondary operating system (a VM) on your host system. Software such as Hyper-V, VMWare, and VirtualBox use these extensions for performance and security improvements.
Disabling IME is probably a good idea in general if you value the openness of your hardware stack. Unfortunately you can't fully disable it at the moment. There are, however, efforts to help you heavily reduce the amount of code running under ME. The
me_cleaner tool allows you to strip most sections of the firmware from the management engine without triggering a signature validation failure or 30 minute shutdown timer. A new trick released fairly recently (actually only a few days before writing this) allows you to disable ME very early and strip out even more code, using an undocumented feature called HAP. The me_cleaner developers are in the process of implementing support for this. Note that both of these tricks generally require hardware modification (reprogramming the 8-pin EEPROM IC which contains the firmware) and are entirely unsupported - you may brick your hardware, although you can always restore the original firmware using an EEPROM programmer.
You can also look into coreboot and libreboot if you want to replace your UEFI/BIOS with an open source option. Unfortunately these projects are generally limited to a small number of old laptops and motherboards.