‘Birth control’ means ‘prevention of births’. Huxley gives as examples, “chemical or mechanical means of contraception”.
So if ‘death control’ is to be understood analogously, it must mean ‘prevention of deaths’. Huxley gives as example mechanisms, “Penicillin, DDT and clean water”. (The second of these has not aged well: most likely Huxley is referring to the use of DDT to combat malaria, but this was much more promising in 1958, before it became clear how quickly mosquitos would evolve resistance. However, we can choose to take it as a placeholder for campaigns of disease eradication.)
Similarly, “religious traditions in favor of unrestricted reproduction” refers to Catholic opposition to most forms of birth control. So by analogy, if there existed “traditions in favor of unrestricted death” then these would take the form of opposition to ‘death control’; that is, to antibiotics, vaccination, clean water, and so on.
Huxley’s argument is that death control is politically easy, because the means can implemented “by a few technicians working in the pay of a benevolent government”, whereas birth control
depends on the co-operation of an entire people. It must be practiced by countless individuals, from whom it demands more intelligence and will power than most of the world's teeming illiterates possess, and (where chemical or mechanical methods of contraception are used) an expenditure of more money than most of these millions can now afford.
In 1958 when Huxley was writing Brave New World Revisited he could perhaps be forgiven for this, as fertility was rising in much of the industrialized world, including England and Wales, where the total fertility rate was 2.5 in 1958, and grew almost to 3.0 by 1964 (ONS). It was hard to see that the demographic transition was coming.