Climate change isn’t caused by just using fossil fuels to make a product, it’s caused by burning fossil fuels releasing greenhouse gasses, (primarily carbon dioxide and methane), into the environment.
Asphalt is a problematic material, but not so much because it’s made from oil. It’s problematic because we burn fossil fuels to harvest the raw crude and to generate the energy needed to refine crude into asphalt. The carbon in the asphalt itself remains sequestered there and doesn’t contribute to the greenhouse effect as long as it isn’t burned later.
If we figured out how to extract crude and generate the vast amount of energy needed to manufacture asphalt without actually burning fossil fuels we’d eliminate the vast majority of asphalt’s impact on climate change.
In fact it’s been shown in a lab that it’s possible to make asphalt from CO2. It’s currently cost prohibitive to do so, but in theory asphalt could be part of the solution to climate change.
Now Asphalt does have other environmental issues, like leaching toxic chemicals into the soil and water table and the fact that it’s usually black which absorbs more the sun’s radiation than almost anything else which would reflect more of the sun’s energy back out into space. But those problems aren’t necessarily solved by using non-petroleum based bioasphault, nor are they unsolvable with bitumen based asphalt.
About 20% of a barrel of oil gets made into products like plastics or foam, that’s not what’s causing climate change. What causing climate change is the 80% that gets refined and burned for cheep energy. So it’s less “Just stop oil” and more “Just stop burning oil”