Problem solved! 
I started to suspect that it might have something to do with the Lua version which is built into Haproxy. The Crowdsec instructions for the haproxy bouncer says that Haproxy must be at least version 2.5. So, I figured I’ll downgrade to 2.6. Lo and behold, now it works!
Hopefully this will be of help to others who want to use the haproxy bouncer. I think it should be mentioned in the CrowdSec installation instructions that later versions of Haproxy might not work correct because of the Lua version.
In conclusion:
Not working correctly:
HAProxy version 3.0
Built with Lua version : Lua 5.4.4
Working correctly:
HAProxy version 2.6
Built with Lua version : Lua 5.3.6
Note: I have tested with hcaptcha. That works fine now. I have not tested the other captchas. But I would guess they too work now.