You may use your college degree in your working life (or st least the fact that you have one) for the next 50 years. That’s too long into the future to try to make sure you graduate from a college that will still exist. And as others have said, even if it doesn’t, it doesn’t make your degree worthless.
That said, there are good reasons to to try to minimise the risk that the college will while you’re still there, possibly severely disrupting your education, or shortly after you have graduated, possibly disrupting your job search or graduate school applications. It probably will not matter once you are established in a career, but while you are still being judged on the education you have completed? It’s just not a good look.
It’s probably a good idea to stay away from any school that has a D ranking in the Forbes lists (in fact, the link is from 2017 and you may find that a number of the D-list colleges have since folded) and look hard at C ranked colleges. Agree that strong religious backing, particularly from a large organization with several schools, may help avoid closures, or at least minimise disruption.
A study has found (not sure if I can link but googling small private colleges closing will find you lots of articles) a number of high risk factors that you can eliminate easily: small private colleges with fewer than 1000 students (the healthiest size appears to be 2000 to 3000 students), small private colleges in New England and the Midwest with regional applicant pools because of declining populations. Also easy to find out: yield and retention rates (bad customer targeting and service), steadily declining enrolment.
So far, top privates with national applicant pools are doing fine, wherever they are. State flagships and strong regional state schools popular among their applicant base won’t close, either. If long term viability of your alma mater is an issue you care about in your college search (and I don’t think it’s a Stupid Reason at all, to reference a popular thread) create your list among those.
From a European perspective, I’d also second those PPs who suggest looking first at what it make you happy to be doing for the rest of your life, and evaluate what you will need to do to get there, which may be college now, or college later, or may be another strategy entirely - reverse engineering the process. I do realise that that is a foreign way of going about it, but it’s actually the international norm, and a perfectly valid strategy for you to choose.
It’s your life. Don’t make your choices depending on others.