For some reason hyperg_2F1_reflect computes the wrong value when c-a-b is integer, and a and b are of opposite signs, e.g.

gsl_sf_hyperg_2F1_e(-0.25, 0.25, 1.0, 0.9, &r)
=> 0.8800433809321181 (should be 0.92058925138209276)

I don't have access to Moshier, so I can't tell if it's due to the "reflection" method or just a bug. However, hyperg_2F1_series appears to compute the correct value for these cases, so a workaround is to use that when a and b are of opposite signs:
https://github.com/ludvigak/gsl/commit/bc27ee844907567bb11b6acc9c6343bfd8ba5438

This appears to fix some of the issues mentioned in bugs #39056, #32306, #21835.

In addition, the fix introduced in commit 9163448f5e0bfa3591a2535c16a2e37386b91171 could use some amendment. First, it uses a stopping criterion of two terms, not the three that Pearson recommends. Second, the new stopping criterion doesn't associate an error estimate with the new termination criteria. This gives an error estimate of O(1) when it's used:

gsl_sf_hyperg_2F1_e(-0.25, 0.25, 1, 0.25, &r)
=> val=0.9833426507751653, err=1.0000000000000049

This can be fixed as:
https://github.com/ludvigak/gsl/commit/da629add7f0a5228dc7ab965c7c6ef88e60486d0