Are you specifying insulation with low embodied carbon? The Zero Energy Project has a great article on the global warming potential (GWP) of various insulation types. In general, those with the most bio-based content tend to be the best and can have a net negative GWP as they sequester carbon.
Rigid and spray foam plastics are at the other end of the spectrum where some use high GWP blowing agents during manufacturing. However, there have been improvements and these agents have been substituted with lower GWP products. For example, there are better versions of XPS and using HFO instead of HFC blowing agents in spray foam reduces the total GWP by about half. Also, wade carefully through marketing materials as some will say "bio-based", yet upon closer inspection the bio-based component might only be 10-20% of total composition.
Finally, many of these insulation materials along with other components can be found in the BEAM tool that helps evaluate the embodied carbon of a building.