> Why do you think allowing incest and increasing birth defects among children is sensible?
Well, first of all, that isn't in fact what I said. I'll come back to that later. Anyway:
As I said in an earlier comment, not everything bad should be illegal. First-cousin marriage is (or at least seems to me) a bad idea; it seems very unlikely to me that its benefits outweigh its costs. But in something that's trying to be a free society we very frequently allow people to do things that are bad ideas.
Do you think it should be illegal to have children when over the age of 35? That causes increased birth defects, I think about as many per instance as first-cousin marriage does. Do you think it should be illegal to smoke cigarettes or drink alcohol while pregnant? Ashkenazi Jewish people have a very substantially increased risk of some genetic problems; should they be forbidden to have children?
I dunno, maybe you do think all those things should be illegal, in which case there's no inconsistency in calling for first-cousin marriage also to be illegal. But I'm guessing you don't, for reasons along the lines of "it's usually better to allow people to do things they want rather than having the government intervene heavy-handedly in their lives". That is also the main reason why it might be a bad idea to make first-cousin marriage illegal.
With that said: I repeat, I did not in fact say that "allowing incest and increasing birth defects among children is sensible". I said that the blogpost is sensible. There is not a valid inference from "document X is sensible" to "everything that document X, overall, seems to be in favour of is sensible".
The blogpost looks at arguments for and against banning first-cousin marriage. It doesn't, explicitly, take a definite position on that question, though it does seem like its author thinks that first-cousin marriage shouldn't be made illegal. I think it's a sensible blogpost; I would think the same if its author had the opposite apparent leaning, if it had the same overall shape of presenting reasonable arguments on both sides. If I think about the matter some more and decide that actually banning first-cousin marriage would on net be a good idea, I expect I will still think the blogpost is pretty sensible.
> I personally imagine it is things like widespread organised rape that was ignored by the police for many years
The Rotherham scandal was scandalous, I agree, and it seems likely that the police deliberately avoided investigating properly because they were afraid of being called racists, and all of that is very bad. But I don't see how you get from there to "therefore the British immigration system is bad". Consider another scandal involving a lot of sexual abuse of minors: the one around Jeffrey Epstein. The people involved in that were mostly (not exclusively, but mostly) rich middle-aged white men. Do we conclude that we should be trying to keep rich middle-aged white men out of the country? Most people don't. Rather, we say: here was a particular network of people, most of whom happened to be rich middle-aged white men, doing Very Bad Things; we should deal with those particular people, and we should improve our systems for spotting Very Bad Things, and if some of those got overlooked because bits of those systems are too generous to rich middle-aged white men then we should change that.
Likewise, in Rotherham there was a particular network of people, most of whom happened to be Pakistani immigrants or children thereof, doing Very Bad Things; we should deal with those particular people, and we should improve our systems for spotting Very Bad Things, and if some of those got overlooked because bits of those systems are too generous to Pakistani immigrants and their children then we should change that.
But being a rich white middle-aged man, or a poor Pakistani young man, isn't some kind of guarantee of being a sexual abuser, and we would do no one any favours by attaching the crimes of the individuals to the whole group and saying: let's get all the rich white middle-aged men out of the country. Or all the poor Pakistani young men.
(In both cases you could make an argument that it wasn't all coincidence that the people came from those particular demographics. E.g., if your mode of sexual abuse involves sequestering the victims on a private island then it's much easier to do if you're a billionaire; some Pakistani communities have traditionally had very high rates of child-marriage and maybe those traditions make men from those communities more likely to become child abusers or something. But in both cases we can also observe that there are an awful lot of rich white middle-aged men and poor Pakistani young men who somehow manage not to abuse any children at all, and conclude that it's probably better to target the crime itself rather than some broad demographic within which we found a bunch of criminals.)
> a steady increase in Islamic terrorist attacks
Yeah, maybe getting up to an average of one event a year, with a total (coming mostly from a couple of particularly severe cases) of something like 100 deaths from terrorism in the last 25 years. Four deaths a year! That's almost one third as many as people dying from having their clothes catch fire, and almost a quarter as many as people drowning in their bathtubs!
Obviously 100 deaths from terrorism is 100 too many. (And 100 deaths from people drowning in their bathtubs is 100 too many.) But, with terrorism as with bathtubs, the number is actually not all that large, and it doesn't make a great justification for large-scale social change such as radical overhaul of the immigration system.
(It does make a great tool for stirring up xenophobia, though.)