Personally I'd make the opposite change (everyone should be exempt) but religious organizations shouldn't get special treatment just because they're religious. The practice of having special rules which only come into play when religion is involved undermines the separation of church and state; it means that the state is discriminating between citizens on the basis of the presence of absence of a (recognized) religion.
> Corporations, and any community chest, fund, or foundation, organized and operated exclusively for religious, charitable, scientific, testing for public safety, literary, or educational purposes, or to foster national or international amateur sports competition (but only if no part of its activities involve the provision of athletic facilities or equipment), or for the prevention of cruelty to children or animals
Religious organizations are exempt from tax, but so are PETA and the ACLU. Against that background, efforts to strip tax exemptions from churches are a deliberate attack on religious organizations as compared to other civic organizations.
There are plenty of other areas where the government shows favoritism toward religious organizations besides 501(c)3 status. For example, ministers are exempt from federal income tax withholding, despite being classified as W-2 employees, and can opt out of Social Security taxes via Form 4361, which is available only to "An ordained, commissioned, or licensed minister of a church; A member of a religious order who has not taken a vow of poverty; or A Christian Science practitioner."[0] (That last one is oddly specific… and goes so far as to endorse a specific religious organization.) Membership in a "health care sharing ministry" also offers, or did offer while it was still in force, an exception to the individual insurance mandate under the Affordable Care Act (26 U.S. Code § 5000A(d)(2), "Religious Exemptions"[1]).
Ministers are exempt from withholding but they still have to pay it, and they pay FICA taxes like self employed workers: https://www.irs.gov/taxtopics/tc417
And that was the point. Other organizations have to be based around some particular beneficial purpose such as charity or education in order to qualify, and that classification can be challenged if, for example, a "charitable" organization doesn't actually redistribute most of the money it receives to charitable causes, but you can start a religious-themed amusement park (charging admission!) and call it a "church" and it's automatically tax-exempt.[0]
> exempt from withholding but they still have to pay it
Which means they're getting several months' worth of extra growth out of that portion of their income than everyone else by paying it at the end of the tax year rather than having it withheld from their paycheck. It's clearly a religious privilege; other W-2 employees would opt out of withholding if they could, but they can't since they aren't ministers.
> and they pay FICA taxes like self employed workers
Despite not being self-employed, and only if they don't use Form 4361 to opt out of Social Security, as I said before. Which is something which can only be done on religious grounds, or a lot more people would be doing the same, as SS is a poor retirement strategy compared to investing the same amount of money privately. (The average rate of return for SS contributions is lower than T-bills, much less mutual funds or stocks.)
[0] https://www.orlandosentinel.com/features/os-holy-land-experi...
There are some historical nuances about power dynamics and avoiding conflict between the church and state, but that is all long ago.
Those are all “Libertarian stances”.