Why don't chilli peppers taste as hot in space?
TL;DR

All food taste bland in space, not only chilli. 



The claim in that tweet ("Chili peppers don’t taste as hot in space as they do on Earth") is not exactly correct because, the way it's worded, it gives the impression that only chilli peppers have a different taste. In fact, astronauts/cosmonauts use more chili and other spices than they regularly do on Earth, for a reason: they say that food in space (microgravity) taste bland. All food, not only chili. 

Since the beginning of space flight, astronauts report that food taste different in microgravity. According to the Scientific American article When It Comes to Living in Space, It's a Matter of Taste (Romanoff and Romanoff, 2017):


  Many said that flavors are dulled and they crave fare that is spicier and considerably more tart than they would prefer on Earth.


So, due to the food tasting so bland, astronauts in fact use more chili and other spices than they normally do on Earth:


  It's possible that hot sauce and salsa could be key ingredients to the success of a manned mission to Mars. The kicked-up condiments already came close to causing a mutiny on the International Space Station (ISS) in 2002 when astronaut Peggy Whitson threatened to bar entry to the crew of the visiting shuttle Atlantis unless they came bearing a promised resupply of the spicy stuff. Only when shuttle commander Jeff Ashby announced that he had the goods did Whitson say, "Okay, we'll let you in then." Whitson was joking, but the need for astronauts to be able to  spice up their food while in orbit is no laughing matter.


However, it's still unknown why food taste bland in microgravity. Also, there is no consensus about that fact, to start with:


  There's little scientific data to back up astronauts' claims that taste changes in space, despite a number of studies since the 1970s on the effect of microgravity on the sense of taste and smell. In essence [...] study participants were split on the matter.


For those that report a change in the taste, some hypothesis were proposed:


  One of the most prominent physiological changes associated with spaceflight has to do with fluid shifting from the lower to the upper parts of the body because of weightlessness. This facial and upper-body swelling also creates significant nasal congestion, and because odor is essential to the sense of taste, a decrease in the perception of flavors would occur.


And also:


  The shuttle has a "sterile" smell, which when combined with other odors, such as the scent of their rinse-free shampoo, can be somewhat distracting. 


However, there is little scientific evidence supporting this fluid-shifting hypothesis. According to Vickers et al. (2001), reproducing that fluid-shift in a simulated microgravity, where people had a head-down bed rest, has no effect on the threshold sensitivity of tastants. The same lack of changes in the taste and smell sensitivity under simulated microgravity was found by Olabi et al. (2002).   

Despite that, this fluid-shifting hypothesis is supported by NASA (Nasa.gov, 2017) in an educational resource for kids:


  From the early 1960s, astronauts found that their taste buds did not seem to be as effective when they were in space. Why does this happen in space? This is because fluids in the body get affected by the reduced gravity conditions (also called fluid shift). On Earth, gravity acts on the fluid in our bodies and pulls it into our legs. In space, this fluid is distributed equally in the body. This change can be seen in the first few days of arriving in space when astronauts have a puffy face as fluid blocks the nasal passages. The puffy face feels like a heavy cold and this can cause taste to be affected in the short term by reducing their ability to smell.


The same source says:


  When food seems to lose its flavor, astronauts usually ask for condiments, such as hot sauces, to give food some intensity of taste. A variety of condiments are available for the crewmembers to add  to their food such as honey, and sauces like soy sauce, BBQ, and taco. (emphasis mine)


Conclusion

For reasons yet unknown, it seems that all food (not only chilli peppers) taste bland in microgravity. To cope with that, astronauts rely on chili and other hot spices. 



Sources: 


Romanoff, J. and Romanoff, J. (2017). When It Comes to Living in Space, It's a Matter of Taste. [online] Scientific American. Available at: https://www.scientificamerican.com/article/taste-changes-in-space/ [Accessed 26 Dec. 2017].
Nasa.gov. (2017) [online] Available at: https://www.nasa.gov/sites/default/files/files/Taste-in-space-TLA-FINAL.pdf [Accessed 26 Dec. 2017].
VICKERS, Z., RICE, B., ROSE, M. and LANE, H. (2001). SIMULATED MICROGRAVITY [BED REST] HAS LITTLE INFLUENCE ON TASTE, ODOR OR TRIGEMINAL SENSITIVITY. Journal of Sensory Studies, 16(1), pp.23-32.
Olabi, A., Lawless, H., Hunter, J., Levitsky, D. and Halpern, B. (2002). The Effect of Microgravity and Space Flight on the Chemical Senses. Journal of Food Science, 67(2), pp.468-478.