Whether or not you should use という[to iu] with a noun like this depends on the exact sentence structure and the placement of emphasis.
To test whether including という[to iu] will sound natural, see what happens when you get rid of the noun being modified, and just nominalize the modifier with the the particle の[no]. If the sentence still sounds fine, you can add という[to iu].
modified noun
環境を守る仕事は、大切だと思います。
Kankyō o mamoru shigoto wa, taisetsu da to omoimasu.
I believe that work that protects the environment is important.
nominalizer
✅環境を守るのは、大切だと思います。
Kankyō o mamoru no wa, taisetsu da to omoimasu.
I believe that protecting the environment is important.
→ This is grammatical, so it’s fine to add という[to iu]!
modified noun
✅環境を守るという仕事は、大切だと思います。
Kankyō o mamoru to iu shigoto wa, taisetsu da to omoimasu.
I believe that work that protects the environment is important.
However, if you cannot nominalize the modifier, including という[to iu] will sound unnatural.
modified noun
環境を守る仕事がしたいです。
Kankyō o mamoru shigoto ga shitai desu.
I want to do a job that protects the environment.
nominalizer
❌環境を守るのがしたいです。
Kankyō o mamoru to iu no ga shitai desu.
I want to do protecting the environment.
modified noun
❓環境を守るという仕事がしたいです。
Kankyō o mamoru to iu shigoto ga shitai desu.
I want to do a job that protects the environment.