The suspects had tried to set a Covid-19 warning notice pinned to the wooden door alight.
There was some damage to the door but the fire was quickly contained.
North Yorkshire Police are investigating the incident, which has angered crews who have continued to attend call-outs throughout the coronavirus lockdown.
Volunteers have had to undertake sea rescues while wearing PPE and while practising social distancing.
Their most recent call-out was over the weekend, when they returned three people to shore after the pleasure boat they were sailing suffered engine failure around six miles from Whitby.