Do philosophers always embrace rationalism? Why not irrationalism? What's so bad about my voting for a political candidate based on how attractive his wife is?

Philosophers are generally speaking fans of reason and rationality, but there are exceptions, e.g. David Hume, who wrote that reason is a "slave to the passions." There is also, often, unclarity about what the reasonable or rational thing to do is. In response to your final question: voting for a political candidate based on the attractiveness of his wife is inadvisable. If human flourishing in the future depends on who is elected, then voting in this way undermines your own interests, not to mention the interests of others.

What underpins acceptance of scientific theories by non-scientists? In a recent argument about climate change, I maintained that, as a non-specialist, I’m not in a position to judge the validity of theories or critiques of theories of anthropogenic climate change but I instead have to make a judgement about the reasonableness of believing in statements that a certain body of people make about the world. My point was that in the absence of any dramatic evidence to the contrary it’s much more reasonable to believe that the IPCC (and almost everyone else) is right than it is to believe either that there’s a huge con or a huge mistake. I think this is right but am I missing something more?

You ask an important question about how non-experts should make reasonable judgments when there is expert disagreement. It is not enough to say that the reasonable choice lies with the majority opinion; the majority has been both unreasonable and/or wrong often enough. I think it is important to look at the case in some detail (although obviously not in as much detail as experts are able to do) and see what kind of evidence the minority is putting forth. That is, are they just nitpicking at the dominant theory, when all theories have areas of weakness, or are they themselves engaged in active empirical research? Scientific disagreement can be productive when both sides are engaged in experiment and observation, but less so when one side is working from an armchair.

Can somebody oppose physical pain (felt by other people) and be indifferent to other kinds of suffering without being irrational? I'm affraid that the answer is "yes": you can hate or dislike anything without hating or disliking anything else, and these are perhaps the best grounds for opposing something. But on the other hand I can't help seeing here some kind of contradiction... What do you say?

What is it to "oppose physical pain" as you put it? Do you mean try to prevent physical pain? But why would you do that? Usually the answer is something like "because it causes suffering". So the reason for trying to prevent physical pain will also be a reason for trying to prevent other forms of suffering. So I think the answer to your question is "no." (Unless you have some grounds for "opposing physical pain" that is different from this usual answer.)