Projectors will, typically, switch in and out of HDR mode. For example, on HDMI2 (HDMI 2.0) my UHD50 will save the settings for HDR mode and use those when HDR is detected, and it will switch into the preset non-HDR mode, and use the preselected settings for that as well. Additionally, the UHD50 will save the settings for signals detected on HDMI1 (HDMI 1.4) and apply those.
However, I think you'll find that projectors may need more tweaking depending on the content, especially with HDR sources, than a TV, because of the non-standard way that HDR content is mastered.