What are the Rosh Yeshiva’s parameters for applying sunscreen on Shabbat/Yom Tov (and do different types/ingredients matter)?
I don’t think it’s refuah, I think it’s preventative. Even if it were refuah, sunburn is definitely choleh kol haguf, so it is mutar. As to memarei’ach, my general rule is that if something is roughly the viscosity of oil then it is definitely mutar, since sikhah is only assur on Yom Kippur, so clearly it’s not memarei’ach. My experience is that sunscreen is not more viscous than that, so it would be mutar.
Many sunscreens are more of a cream. They do not pour like an oil and stay in one place if you do not spread them. Would that change your analysis? We have generally used a spray on Shabbat, which would be more consistent with an oil as it goes in wet and runny. How hard should one try to find such a sunscreen?
Spray is definitely better. If it’s a cream, then dab it on in different places, don’t smear it. Pat your face, arms, and legs with a towel. Don’t move the towel around, using it as a means to smear, just put it against your body and let the spreading of the dabs happen by themselves.