I would be inclined to give in to a reasonable Demand from Ragnar or Cathy, since either of them will almost always (80% chance) plan a Sneak Attack upon a Demand being refused. Sneak Attacks suck because they only really declare when they know that they have a good advantage, such as being able to take a City amphibiously.
On the contrary, an Honourable War Declaration often leaves the AI unprepared... whereas Ragnar has a 20% chance of pulling one of these, Cathy has a 0% chance.
So, unless they ask for something big or ask for a tech that leads to Feudalism, I would be tempted to give in to either of them making a Demand, at least until we're strong enough to take them on in a fight.
Isabella is also one to watch out for, with a 60% chance of a Sneak Attack and a 10% chance of an Honourable War Declaration.
Joao has a 40% chance of a Sneak Attack and a 10% chance of an Honourable War Declaration for a refused Demand, while Willem's numbers are 50% and 10%. We probably want to weigh the size of the gift against the trouble that we'd face if either of these two declared war on us.
Vicky has a 0% chance of either a Sneak Attack or an Honourable War Declaration if we refuse her Demands, so there's no harm in refusing any Demand that she makes.
If an AI asks for Meditation and they already have Priesthood, then I see no harm in giving it to them. On the contrary, if an AI does not have Priesthood (such as Cathy), I would not give that AI Meditation. Along the same lines, I wouldn't give out Priesthood, Monotheism, Polytheism, or Mysticism.
As for Joao... we might as well wait for Currency before giving him Math, so that it can count as a trade instead of a gift by getting a bit of Gold for that tech. I mean, if you seriously want to be able to get some techs in trade, we need to be careful here: we currently have alienated 3 AIs from wanting to trade with us; we don't want to do the same with Cathy, especially since Cathy has a very low Monopoly threshold (i.e. she will trade techs quite readily, almost as readily as Willem would).
Joao is a bit of a Monopolist anyway (he's a 40% Monopolist--the second worst in our game, after Isabella), so it's not like we really need to try and get on his good side by giving him a gift... he probably won't give us techs in return no matter how much we try and please him. And if we anger Cathy by gifting Math to Joao, then what's the point of gifting Math... I mean, if the AIs will research techs but we won't be able to get the techs in trade because too many of the AIs hate us, then we will have defeated the entire purpose of gifting them Math.
So, with future trading possibilities in mind, there's another reason to accept Demands from Cathy and Willem: they are by far our best chances of any of the AIs in terms of being able to get techs in trade from the AIs.
In other words, I think that we should have a more flexible Diplo policy than "simply refuse every Demand."