At least in the early 20th century, multigenerational Irish, German and Italian immigrant households in New York were all fairly common, so I find it hard to square with what you're saying.
https://en.wikipedia.org/wiki/Western_European_marriage_patt...
I attribute that to widely available "free" University education (women were equally represented in student populations, if not at 50%, at 45% for sure, though "citation missing") soon after the World War 2, housing availability, etc.
So the Hajnal line is trivial to disprove by just looking at numbers for a single country East of the line like Serbia: https://en.m.wikipedia.org/wiki/Demographics_of_Serbia
Knowing some internal details like the fact that Kosovo probably had highest fertility in Serbia until it split off, the situation in 70s probably mirrored the one from countries West of the line.
The pattern Hajnal notices more likely corresponds to migration into cities (move from agriculture to industrialization and now services) and wider availability of education and employment to everyone, but in particular women (which happened in Communist Yugoslavia) and rising standards of living, rather than historical cultural traits as he claims in his paper (though I found only an abstract).
With more effort and closer look, I am sure that all of this could have been disputed even in 60s when the paper was published.
And interestingly, more recent data suggests that West of the line now has a higher fertility than the East in Europe.
[0]: https://en.wikipedia.org/wiki/Hajnal_line
This has been true for at least a thousand years. America was largely settled by people from this folkway.
The influence that this pattern, and the bans on cousin marriage (out to fifth cousins in some cases, but second cousin marriage was commonly forbidden), has had on what we sometimes call WEIRD people, is interesting, if a bit off topic.