I recently worked on a project where I had to choose a hash function for non-cryptographic error checking. I investigated CRC in detail for it, even wrote two different implementations from scratch.
CRC-X is complicated to use and terrible choice.
First of all, it is not a single algorithm, it is a family of algorithms. For a CRC of size N, you have to also choose a N-bit polynomial, N-bit starting value, and N-bit output XOR value. There is no single standard, there are tens or hundreds of popular options [1]. The optimal polynomial depends on both the CRC size, and the length of the data you are feeding into it [2]. If you choose poor parameters, you will get terrible error detection characteristics (like allowing extra 0 bits at the start of data with no change to the checksum). If you choose good parameters, certain classes of common errors like zeroing out a block of more than N bits will still have much worse characteristics than 1 / 2^N random chance of collision.
Second, implementation in standard libraries is patchy. Most programming languages have some CRC32 implementation - but do not document what parameters they use, or use different notation for the same parameters (forward and reverse), or do not let you change the parameters, or do not let you change the CRC size, or all of these. There is no easy way to get a "standard CRC64 or CRC128" compatible across platforms without putting it together from github snippets and example code yourself.
Third, CRC is fast when implemented in hardware, but not that much faster than SHA-1 or SHA-512 in software. It's only 1.5-2.5x faster [3], and when you're doing one checksum per uploaded file or something, it really does not matter. It's going to be even slower when you don't have a suitable-length CRC available in optimised native code, and have to write it yourself in simple C or pure Python.
The obvious and simple solution is to pick a known popular cryptographic hash like (SHA-X) that is available in the standard library of every programming language under the exact same API and no parameters to configure, truncate its output to the digest size you want, and call it a day. No need to worry about error detection performance on specific error cases like long bursts of zeros, and you get some defense against malicious tampering as a free bonus.
[1] https://en.wikipedia.org/wiki/Cyclic_redundancy_check#Standa...
[2] http://repository.cmu.edu/cgi/viewcontent.cgi?article=1672&c...
[3] https://www.cryptopp.com/benchmarks.html