This is only true on the energy and transportation sides of emissions. Some processes like the creation of cement and refining of steel create CO2 through chemical processes, regardless of the energy source.
Also, note that 70% of steel production in the US isn't from ore at all, but is from scrap metal. Most of the steel used in renewable energy infrastructure will not be consumed, but will be recycled.
For context, the US contributes less than 10% of the steel production of China to global crude steel production figures.
And also, that carbon is not going into the atmosphere as carbon dioxide — it's going into the steel (as iron carbine and graphite IIIRC).
I think there are at least two ways to make lime without CO2 emission. The first is normal limestone calcination, but with CO2 capture. The other is to use calcium silicate. This means dissolution of the silicate with hydrochloric acid, separation of silica, then high temperature reaction of calcium chloride with steam to produce lime and hydrogen chloride. I understand there's a company trying to commercialize this latter process.
That said, there's a difference between sourcing that carbon from fossil fuels, carbon "new" to the current land|sea|atmosphere cycle having been drawn up from where it was sequestered millions of years past, and carbon that is already part of the surface dynamic.
Major steel players, those in the billion tonne per annum mining and processing chain, are already going hard at replacing current steel making with several alternatives and have already built pilot plants to trial low | zero "new carbon" production techniques.
eg: Rio's BioIron: https://www.riotinto.com/en/news/stories/decarbonising-steel...
is one such trial, IIRC that link mentions others.