Continue effort to show concrete evidence of the effectiveness of CL methods, such as obtaining internal and external grants, seminars where actual students projects are shown, etc. seem to lower the level of downplaying by traditional professors Nothing major. The problem doesn't come so much as a conflict between different styles in different sections. We are a small enough school that we do not often have multiple-section courses. However, we have experienced some difficulty with instructors in the client disciplines making disparaging comments. There is more conflict about the use of technology than cooperative learning.
Most instructors are open but skeptical about grading standards.
When I was a graduate student at an large University -Yes. But now that I'm at a smaller institution, No. I think it depends on how many sections of a course are available for students to take. The conflicts haven't started yet, but I can see them arising in the near future. The major conflicts I have experienced had to do with the problem of peer evaluation of instruction.