According to the definition of PointReflection provided in the announcement of the Sake tourney 2019:
Only non-reflected K and R can castle

Bug: With Popeye 4.83, K and R can castle when they are reflected.

Could you solve this issue?
I think that the intention of the inventor of the fairy condition was that King and Rook cannot castle when they are reflected by another piece (King not reflected by King, Rook not reflected by Rook).

Example with white King e1 and white Rook h1 reflected by different black units on d8 and a8 (it works with any kind of unit on d8 and a8) :

BeginProblem
Pieces
White Ke1 Rh1
Black Ka8 Rd8
Stipulation ~1
Condition pointreflection
Option MoveNumbers NoBoard
EndProblem

Popeye result:

1 (0-0 Time = 0.017 s)
1.0-0 !
2 (Ke1-a1 Time = 0.019 s)
3 (Ke1-b1 Time = 0.021 s)
1.Ke1-b1 !
4 (Ke1-c1 Time = 0.022 s)
1.Ke1-c1 !
5 (Ke1-d1 Time = 0.022 s)
6 (Ke1-e8 Time = 0.023 s)
7 (Ke1-e7 Time = 0.024 s)
1.Ke1-e7 !
8 (Ke1-e6 Time = 0.024 s)
1.Ke1-e6 !
9 (Ke1-e5 Time = 0.025 s)
1.Ke1-e5 !
10 (Ke1-e4 Time = 0.027 s)
1.Ke1-e4 !
11 (Ke1-e3 Time = 0.028 s)
1.Ke1-e3 !
12 (Ke1-e2 Time = 0.029 s)
1.Ke1-e2 !
13 (Ke1-g1 Time = 0.031 s)
1.Ke1-g1 !
14 (Ke1-f1 Time = 0.033 s)
1.Ke1-f1 !
15 (Rh1-g2 Time = 0.044 s)
1.Rh1-g2 !
16 (Rh1-g1 Time = 0.049 s)
1.Rh1-g1 !
17 (Rh1-h2 Time = 0.055 s)
1.Rh1-h2 !
solution finished. Time = 0.056 s