Solution
Dumped 32 bit CentOS 7 and installed 32 bit Ubuntu 16.04 LTS which seems to be the last 32 bit Ubuntu LTS.
No kernel panic is observed with 32 bit Ubuntu 16.04 LTS while installing Rust or building/running Rust applications.
History
This 32 bit machine previously had Ubuntu 12.04 LTS and 14.04 LTS and the experience was smooth. So, 16.04 LTS looks to be a sensible choice.
Service/update
The only problem is that Ubuntu 16.04 LTS is going to be out-of-service in April 2021. So no more updates! To work around that, another solution might be to install 32 bit Debian on the machine. The machine didn't have any Debian before, so anything might happen :(
Final solution
openSUSE Tumbleweed 32 bit
Eventually I installed openSUSE Tumbleweed 32-bit which is updated regularly due to being a rolling release. It works great =)