My starting point is open access for all, however I realise (and there is allowance for this in the CRoW act), that certain areas should be of limited access or off limits for various reasons. This could be delicate flora or fauna, or geophysical features. I would imagine that these would be relatively small features within the landscape, or that whole area would not be designated open access land. As far as gates on caves go, they should be the last resort after other avenues have been tried.
For example, if you are heading for a cave on the fells, you will probably have a fair amount of info before you go; location, rigging guide, survey etc If in the same places it was stated that such a site is to be avoided because of cave life, delicate mud or stalls, being a water supply, etc I would hope as a responsible caver the trip would be rescheduled. There is provision for scientific endeavour to ensure the reasons are still valid, or for other reasons. Only if a location is being damaged should a gate be considered as a last resort.
I am aware of a nationally important bat roost, also being historically significant, that has several gated entrances, and a couple of open ones as well. Sad to say certain groups feel it acceptable to have midwinter rave parties with fireworks, fire breathing, music, lighting, large crowds, cooking and sleeping over. The waste (of all sorts) is never removed and much vandalism such as spray painting and pulling down of stacks of rocks, even historical features, seems de rigeur. The bats of course are not happy and the history is degraded. Attempts to rectify this are often sneered at and actively discouraged