I would have thought that the workers at GitHub would know as much as anyone that restricting access to one Git service would have a negligible impact on ICE. The real impact would be on GitHub themselves, as they would lose any opportunity to help guide policy or technology at ICE or any other government agency. It may feel better to watch and yell from the outside, and you may have the moral high ground in doing so…
There's about a 0% chance that a government agency would change anything about their policies based on what GitHub employees say. Companies that work on government contracts get "report cards" detailing the agency's satisfaction with their performance, and any other government agency can view the reports for that company, so it's in their best interest to try and get favorable reviews by doing what the agency wants.