I doubt you can find a plan that does not cover abortion and birth control.
I don’t see how you would be obligated to not carry insurance because of the coverage of the plan. You have no say in that.
However, it is very important to carry health insurance, even if it has a high deductible with an HSA account. That is the type of insurance we have.
One reason to carry insurance, no matter what, is that if you are insured then you will be charged by doctors, hospitals, labs etc. the “negotiated rate” for these procedures that the health care providers have negotiated with the insurance companies. The negotiated rate is much less than the providers’ standard rate that you will be charged if you don’t carry insurance. The negotiated rate could be half the standard rate, or even less than half the standard rate for some lab tests.
Thus even if the bill is paid by your HSA account, the amount you will be charged and pay will be ~ half what you will be charged if you don’t carry insurance.
Also, HSA accounts can grow if they are not used, and can later be used for many health care expenses including long term care insurance when you get older. HSA plans are usually much cheaper than plans without an HSA, and the difference in premium goes into the HSA account, that you own.
Good luck