HAProxy is a TCP/HTTP load balancer, so the entire perspective of the software (from configuration to feature emphasis) stems from that.

Squid is a caching HTTP proxy, which began with forward proxying but also supports reverse proxying. I wouldn't regard it as relevant to modern, dynamic architectures as HAProxy or Varnish (another caching-focused project).

There's no real difference in open source purity between any of these projects, unless you dislike the stewardship of a company. HAProxy has existed for a long time without such stewardship (as has Varnish). Indeed, Squid's lack of commercial backing might be a hint as to its current relevance.