So in summary, these are the big issues:
Substantial burden analysis is empty. Just claim that something burdens your religion, and the Court is fine with you relying on blatantly false statements (x pill is an abortifacient) and does not care if you rely on illogical leaps (an employee using an insurance card I gave them to purchase birth control affects my religious beliefs but an employee using the paycheck I gave them to purchase birth control does not) or attenuated connections (even if I never know whether an employee ever uses their health insurance to use this particular contraceptive, my religious beliefs are still burdened).
The religious non-profit workaround was crucial to the majority’s decision that there is a less restrictive means available. But that workaround is also currently being challenged as a violation of RFRA. What will happen if the workaround is struck down too?
Corporations now have an incentive to adopt anti-healthcare religious beliefs in order to avoid paying for insurance coverage. Each healthcare procedure/prescription will have to be analyzed under strict scrutiny, to see whether the government actually has a compelling interest to see that you get that kind of coverage and whether the government has used the least restrictive means possible to provide you with that coverage. It would be far simpler to go directly to a single payer system—but we’re not getting that through Congress anytime soon. The Court has thus empowered the Religious Right to chip away at the ACA case by case.