Can anyone share references, where it would be confirmed or disproved that, despite the theoretical identity of BER, in practice BPSK is a more stable type of modulation compared to QPSK?
I just googled bpsk vs qpsk: here's one of the references you are looking for:
Performance analysis of BPSK and QPSK modulation schemes for different channels conditions in GFDM system by Randy Verdecia Peña
ISSN 1390-6712, DOI: 10.24133/maskay.v8i1.506
The article is in Spanish but it starts with an executive summary in English where it states what you want to confirm. You can also check that BER is different for both modulations (due to the sin(PI/4) factor in QPSK). Also, though the article talks about using these modulations under GFDM, the conclusions about the robustness of BPSK vs QPSK are logical; the wider separation of symbols for BPSK make it more robust in exchange for power and bandwidth efficiency. There's always a trade-off to be made.