WD40 is the right choice.. for indoor
grease for outdoor gate if it expose to rain, becoz it would get wash off..

Just applying my common sense

yes. but they dont dont come in spray application. cant reach tight corner

WD40 is a brand. they have lot of range do different use case. what you are looking for this case is WD-40 Specialist Product High Performance Silicone Lubricant

silicone not just for rubber, it works on all material as it is stable compound, just the adhesion to metal is not as great as white lihium grease, but for slow moving stuff, should not be much issue. for things like door or gate hinge, pulley or trolley wheel, silicone lubrication i find it better. I usually use white lithium grease for those bicycle and motorcyle gear and other fast moving metal gear stuff. but ya, if you want, sure white lithium grease, sure.

i use this for my bike chain. find it easier to spray.