It feels like any process that requires discipline, they'll run away from. Theres even tribes of people who will intentionally group all tests as "unit tests." There are other tribes who will try to write all integration or feature tests as "their unit tests". It's pretty frustrating to see a ridged and very well defined group of tests get ignored.
However it will matter a lot on where you spend your effort on, and whether your environment understands why it matters. If you just mention "I'm writing integration tests" - and nobody knows why it's important to do that right now - it will likely not go too far. However if it's along "we have this regular operational issue that everyone in my org including the director was aware about, I fixed it, added integration tests, and made sure I added automation that will catch further regressions before our customers will observe them" - it will go a long way.