Are MESFET transistors still used in the industry?
Short answer:
I cannot speak for discrete parts by direct experience; however, we've make MESFETs a few times because you can tweak some standard SOI processes to make them.  We used them on the periphery as drivers.  I'm pretty sure that a discrete part would use a HFET (https://en.wikipedia.org/wiki/High-electron-mobility_transistor) as they'd be cheaper to make as singles and have better drive performance.

Longer answer:
This is a conjecture, but I'm pretty sure that I am correct, and I will happily take any censure on the topic.

While the MESFET would be the most mature device, the "electron mobility transistor" (HFET, emtf, etc) class is similar in behavior, but would have better noise and power performance as the channel is driven by the surface concentration of electrons and the channel isolation is key to having a strong power driver with low noise.

The HFETs use the "MOSFET" architecture, and the presence of capacitive coupling between the gate and the channel, which results in the overall noise being determined by subtracting part of the gate noise from the drain noise. This physical property of MOSFETs leads to very low noise performance and  thermal-diffusion noise is a result of random variations in carrier speed in the device channel.  The MESFET looks more as a JFET and I would expect the device to have lower flicker noise, but higher noise switching and less control via the gate.  The architecture will have higher noise due to impact ionization at higher power levels as well.  This is also a problem with MOSFET architectures, but I can use heterojunction barriers to decrease the number of holes that are causing impact ionization and tossing electrons back up toward the gate.  With a JFET-style gate, I cannot think of a way to mitigate this. 

The isolated channel from the gate in a HFET also means that you will have better amplification.  This is from the fact that the doping of the source/drain regions have more flexibility because the gate is isolated from the channel.   

This is not a great answer, but it's the most nearly correct one I can give you.