Is intelligence compatible with compassion?

Yes, they are deeply intertwined.

Short answer: Compassion without intelligence is useless; Intelligence without compassion is dangerous.

Long answer:

As all beings are interdependent, egocentrism and selfishness are not truly intelligent behavior. Of course you need to have self interest, so you can take care of yourself, but not in excess. It would be silly to let yourself die because you're compassionate and peaceful in relation to, e.g., a person who's trying to kill you.

However, as another example, it would be very dumb to accumulate more material resources than you need to survive and not use them to set the wheels of the world in motion by investing in good projects (those that address real problems, not imagined ones).

True compassion demands higher intelligence. First, because being able to put yourself in someone else's place requires an outstanding ability.

Then, a remarkable intelligence is needed to figure out what you can do or not about their suffering, and in the case you can't, to being able to refrain from silly compassionate acts.

A clear example would be to do whatever a child wants without ever putting a limit. Reality is full of limitations and the sooner you help children to understand it (but without being a jerk, too), the better they will deal with life.

This is completely natural, so many religions have visions on it, but they're not at all a sine qua non condition for it. Actually, they usually become obstacles for developing compassion and intelligence. In the moment you adhere to a religion, you're risking being non-compassionate and unintelligent, because of the divisions you automatically arise between you and the others. Not to mention the self-righteousness and other stupidities that usually come with the package, with few exceptions.

When you nourish beliefs not based on reason, logic, facts and evidence, you're not being intelligent and compassionate, too, because this would lead to false assumptions on reality that could deter or even block true solutions to real problems.

The same could be said about dry intellectuality. In general, it is very limited because it turns into puerile pride that creates division between you, others and the world. Reality has so much information that no one – not even the most intelligent being in the whole multiverse – would be able to acquire more than a tiny fraction of it (because no being can equate the universe or will become the universe itself). Besides accumulating information, it's also needed to reflect upon the data acquired. So, there's always something to learn, even from the worst of all beings.

That's why the great philosopher Socrates said that “All I know is that I know nothing”. Of course he knew a lot, but he was pretty aware that in the moment you start feeling prideful about your intellect, you start to crumble into the inability to keep learning.

This doesn't mean that we can equate faery tales to truth, but it keeps you immune to other people's pride when they try to make you eat their fables as if it was absolute truth. This essential awareness opens you up to good humor about difficulties (including prideful rationalists) instead of recoiling into pride for detecting someone else's bullshit.

Then, if you're not able to really help them to awake from their personal nightmares of prideful selfishness, you refrain from silly compassion and just laughs about that.