It was rational for the very Powerful to fear the very Weak, if weakness (degeneracy) was indeed infectious and then inheritable ...

If your basic (often unconscious) assumptions are plum-dead crazy, as they usually were during the 1860s-1960s era of Panic Modernity, it matters not how logical and rational your subsequence arguments are.
This was definitely the case with the way Modernity thought about contact with people who had physical, mental or moral weaknesses.

There is no evidence that your daughter marrying a man who had Rheumatic Fever as a child lead inevitably to her children receiving his 'gene' for rheumatic fever.

In any case, the ill effects of this particular once very common disease could always be greatly reduced and the disease is now so successfully preventable as to be almost unknown to current generations of parents --- there is nothing truly 'infectious' or 'inevitable' about it.

Only a tiny (but definite) contribution from one's genes helps bring on Rheumatic Fever - it is mostly a disease caused by overcrowded and ill-ventilated homes and then poor medical followup, both the result of poverty and prejudice against minorities and immigrants.

But Modernity was an era when most people actually thought a grandparent who started into drinking too much would pass his resulting alcoholism on to his kids and their kids --- so marrying an alcoholic's kid was seen as a personal disaster and a disaster for the nation and race.

TB, mental illness, criminality, laziness, free and easy female sexuality, along with an ever growing list of chronic and congenital illnesses, were seen as inevitably inheritable.

Worse : all these people who were seen as inevitably and permanently defective, unfit, degenerative ---- unable to really do useful work or fight in a war --- were still seen as able (thanks to the power of romantic love) to steal the bride/groom intended for your loutish ultra-fit children and then proceed to breed lots of new degenerate offspring, like defective rabbits.

Love - romantic love - led to sexual intercourse between the unfit and fit, which was really a 'genetic infection' and thus led to race suicide

The only weak people the powerful of Modernity didn't fear were those who were certifiably unable to conceive children - those unable to 'genetically infect' the strong - those who had been sterilized by a doctor. 

The important thing to realize is that the strong feared the weak more than they fear other strong people, because they saw the weak has having a "weakness" that was both inevitably successfully infectious (rather like a germ-borne disease) and inevitably inheritable (based on the overly simple - and simply untrue - picture of genetic inheritance still taught to all school kids).

It was a story that always played out as a one-way downhill contest : the mildest of weakness genes would inevitably beat out even the strongest of strong genes.

(Recall the widely held beliefs that even a one time one drop of negro or jewish blood would be enough to ruin the strongest of Aryan families forever on into eternity.)

One sees here the perhaps half unconscious creation of a 'total exclusion' taboo, really designed to ensure that no child never ever ever tries out marrying a Jew or Black , only to find out that the world didn't suddenly end in blood and fire, as their parents had always warned.

The danger with this sort of total exclusion taboo barrier is - as always - that even one exposure of a parents' cry of 'wolf' as being a total lie can lead to a equally total rejection of all those parents' values.

I believe an example of this happened, just after WWII.

Boomer kids, such as myself, soon learned that the previously much hated 'parasite' fungus produced the wonderful lifesaver penicillin while the previously much honored chemists of Germany produced only Auschwitz's horrific killer Zyklon B...