Firstly, I would like to note the source you are looking at. It is a very right-leaning news source that has a lot of conservative bias. Secondly, I would like to note the claims the article makes:
1. Birth rates are plummeting in the US.
2. Other countries including Hungary and South Korea have had the same problem and supplied government aid to families to support people in having more kids.
3. Expenses of having kids is not connected to the birth rate decline because in the past there were higher birth rates even when people had less money.
4. Higher education policies make it so people stay in higher education for longer creating an "Extended Adolescence"
5. Religious schools not being funded by tax dollars creates a barrier in accessibility, which decreases the importance of religion which also decreases birth rates.
Fact-checking the claims:
1. For the first claim this is true, according to the CDC we have seen an all-time low for birth rates in 2022 and 2023
2. Hungary did create a program where women with four or more children would be exempt from paying income tax and in 2019 the average number of children a Hungarian woman will have in her lifetime is 1.45. The fertility rate has continued to increase since 2019 which wasn't noted in the article. In South Korea it is also true that they have worked to aid families who have kids with more work benefits and help with education costs, which started in 2022. While South Korea still has a very low birth rate of 0.75 in 2024, it has started to increase which is a start.
3. In the past it is true, expenses did not affect birth rates. But in recent years richer countries have had higher birth rates. As well government programs that aid parents who are also working benefit more than other programs
4. While there are some talk about college creating a new extended adolescence it doesn't seem scientifically backed. There is truth behind people being older when they have kids. This seems to be linked to women wanting to get a handle on their career and feel like they have the financial stability to have kids.
5. With this argument, I think it gets very close to breaking the First Amendment; to make no law respecting an establishment of religion. Which mostly negates an argument about public funding to religious schools. While there is truth to the fact that there are higher birth rates among religious families. But with this data, there is not a lot to be done on a governmental level so it is not as valuable in this argument
To conclude there is some truth to the article, it's conclusion it gets to is not linked to actual data and it ignores a lot of actual data points or parts of the facts to get to the conclusion. In actuality giving funding and support to families who need the financial stability to have kids would possibly help more than just getting rid of funding all together.
Sources:
https://www.cdc.gov/nchs/pressroom/nchs_press_releases/2024/20240525.htm
https://www.bbc.com/news/world-europe-47192612
https://www.macrotrends.net/global-metrics/countries/HUN/hungary/fertility-rate
https://www.thinkglobalhealth.org/article/south-koreas-plan-avoid-population-collapse
https://www.reuters.com/world/asia-pacific/south-koreas-policy-push-springs-life-worlds-lowest-birthrate-rises-2025-02-26/#:~:text=In%202024%2C%20however%2C%20the%20glum,try%20to%20reverse%20the%20trend.
https://www.imf.org/en/Publications/fandd/issues/Series/Analytical-Series/new-economics-of-fertility-doepke-hannusch-kindermann-tertilt
https://www.northwell.edu/news/the-latest/geriatric-pregnancy-increases-complication-rate#:~:text=New%20moms%20are%20trending%20older,Center%20for%20Health%20Statistics%20data.
https://ifstudies.org/blog/americas-growing-religious-secular-fertility-divide