As a stopgap until I write specifically on this question, here is an extract from my PhD that addresses it in passing.
Natalism is the advocacy of a high birth rate within a community. Urging parents to have additional children is an obvious manifestation, but there are other parameters affecting the birth rate and efforts to influence these can also be natalist.*1* These proximate determinants of fertility concern womens’ lives and are primarily the percentage who become mothers, the age at which childbearing starts, and the duration of any interruptions (child spacing).
In traditional societies these are shaped by the proportion never marrying, the age at marriage,*2* the interval before widows remarry, physical infertility, and the fertility-suppressant effect of breastfeeding (postpartum infecundability) which was extended for two years or more in many cultures. How much other methods of family planning were used in pre-modern societies is debated.
In the modern world contraception became (and remains) very significant. Other factors still contribute to limiting births, but late marriage is far less important than it once was because with a small ideal family size most women complete their family despite starting at a later age.

From page 262 of Baird, David. “Fertility and Ageing.” Human Reproduction Update 11.3 (2005)
261-76.
However within US natalist subcultures, aspiring to a larger number of children, age again becomes important. The graph overleaf of births in (pre-modern) “natural fertility” populations (Baird 262) shows why age at marriage, and spacing between successive children, are determinants of completed fertility among natalists.
All the factors noted above can be regarded as levers potentially usable by natalists to influence birth rates.

A minor factor but one with rising significance, especially in the USA and Israel, is medical treatment of infertility. For example, Susan Kahn finds that a “convergence of pronatalist social pressure, rabbinic permission, and economic accessibility makes fertility treatment all but inevitable for infertile ultraorthodox women in Israel” (294). By contrast, I have not found advocacy of fertility treatment among Protestant natalists, on the contrary some oppose it as unnatural.*3*
I make a distinction between effect and motive, and describe below seven ideas which in practice raise birth rates but are not necessarily natalist. Any of these ideas can be held independently or in combination with others. The ideas are:
first, that marriage is normative, and most people should marry;
second, that youthful marriage is the ideal;
third, that seeking to reproduce is essential to the constitution of a valid marriage;
fourth, that any conjugal act without intention to reproduce is perverted;
and fifth, that sterilization is self-harm.
The sixth and seventh ideas condemn the use of artificial contraceptives*4* and procedures leading to abortion.
In practice these ideas may increase birth rates, for example by disparaging singleness, encouraging earlier marriage, stigmatizing the childless, and hindering family planning.
However they should not be classified as natalist unless the writer’s motives include a desire for high fecundity.*5* If the expressed concern is instead only about, for example, promiscuity, self-harm, fornication, selfishness, or killing the unborn, then the idea is not natalist, even if based on the same OT fruitful verses.
The first and seventh ideas are common among conservative Protestants. A small minority of Protestants adhere to the fourth idea (procreationism) and so avoid family planning: most of these are also natalist, and they can be called unlimited natalists.*6*
The distinction between natalism and beliefs that incidentally affect birth rates will now be clarified. The fourth idea, that a conjugal act must intend reproduction, is called procreationism. Kathy Gaca (94, 255) finds its roots in Pythagorean eugenics, as transformed by Philo, adopted by Clement of Alexandria, and moderated by Augustine for whom fallen marital sexuality is a venial sin excused by the good of offspring. That is far from natalism (Augustine preferred abstinence (and even abstinence within marriage) above reproduction, as chapter 5 will show), and Catholicism now permits Natural Family Planning (NFP) as implied by Casti Connubii in 1930 and clarified by Pius XII in 1951 (Zimmerman 8). Humanae Vitae in 1968 contrasts two couples who are both “attempting to ensure that a child will not be born,” that is both have contraceptive intention, but only the couple using a method of timed abstinence is deemed to be acting morally: this is compatible with planning a small family size. Conversely, most Protestant natalists accept routine use of artificial contraceptives for timing and spacing births while advocating a high birth rate and large family size.*7*
The condemnation of intentional childlessness is not necessarily natalist. Many modern Protestants believe the “unitive and procreative ends of marriage” must not be divided but argue this applies at the level of the whole duration of a marriage (Mangina 476). This appears as the third item in the list of ideologies above. The implication that a deliberately childfree marriage is wrong is emphasized by Thielecke and others (Poulson 154). Where that is the only reason, urging such couples to have a child is not natalist, but the same exhortation if rooted in a desire for high birth rates would be natalist; and it could be a tactical step prior to urging higher reproductivity. The same is true for all seven of the ideas I noted as incidentally affecting birth rates. When they appear in writings that also advocate high fecundity, they function as part of a natalist agenda.
*1* I will ignore determinants such as the age of menopause, maternal mortality, and disease, which either vary little across a modern national population, or are not amenable to change through natalist exhortation at the individual or sectarian level.
*2* Phrases such as “age at marriage” continue to be standard terminology in demographic literature, though reproductive relationships other than marriage are included in the data under these euphemistic headings.
*3* An exception is vasectomy reversal, which Protestant natalists recommend.
*4* Arguably this might not raise fertility even in effect as well-trained practitioners of Natural Family Planning can apparently prevent conception as effectively as users of artificial contraceptives (Zimmerman).
*5* In demography “fertility” refers to the number of births and “fecundity” refers to a potential parent’s physical ability to reproduce, whereas in medicine the latter is referred to as fertility. I will use both terms as synonyms referring to the number of births.
*6* Many unlimited natalists identify themselves as “Quiverfull” (Joyce 134).
*7* The use of contraceptives to increase the surviving number of children (in situations of subsistence poverty) is further indication that anti-contraception is not the same as natalism.
Extract from pages 2-5 of John P. McKeown, “US Protestant natalist reception of Old Testament fruitful verses : A critique”, PhD thesis, Liverpool University, 2011.
Bibliography (for whole thesis), other downloads, and outline of chapters are archived online at University of Chester.