If you shoot RAW, the in-camera white balance does not change the RAW data itself. It mainly affects the JPEG preview and the starting white balance your RAW software shows when you first open the files. You can fully change WB later in post.

For consistency between two shooters, avoid Auto WB if matching files is important, because it can vary from shot to shot and between camera bodies. A better approach is to use the same white balance setting for the same lighting, or set a custom white balance from the same white/gray target when the light changes. If conditions are changing quickly, keep one setting for a while and reset when the light meaningfully changes.

If you use different camera models, matching may still differ slightly even with the same WB setting. In that case, shooting a gray card or color checker reference can help you synchronize color more accurately in post.