In DH's culture, first cousin marriages are traditional. Parents often will arrange marriages to first cousins - in many families, it is often assumed from birth that .first cousins will marry.
DH and his parents are REALLY opposed to this because not only does it cause physical health issues (DH's father has several minor birth defects which are really common in their community, as do several of his family members, as a result of this. He is extremely self conscious about the defects which make certain tasks more difficult, although not impossible. Interestingly, culturally these birth defects are considered lucky, although of course many individuals don't agree/don't feel lucky, like DH's father.)
But another big issue is from a mental health perspective. Another big part of their cultural traditions is that cousins refer to each other as 'brother' and 'sister' and are raised very closely, like actual brothers and sisters. DH gets really upset when he talks about this - being raised as brother and sister, and then suddenly told you have to marry when you reach a certain age. He thinks it's close to sexual abuse. Luckily for him, his father was already against this tradition due to the physical health issues he has, so this was never an issue for him, but it's upsetting enough for him to even contemplate that traditionally he should marry his own 'sister' (again, cousin, but they were raised as siblings).
Now both us and DH's siblings have children, it also has made the family even more opposed to this practice - the idea of the children getting married one day is upsetting and disturbing to us all, but there have been comments made by elderly relations about it! So there is still pressure, although the practice is becoming less common as people start to realise the health implications and become more aware about issues like abuse, consent, etc because of the internet and coming into contact with people from different cultures who don't have these traditions.
It is very much not the case that this is something popular even within the cultures where it is practiced, and although traditions are considered important, they can still cause a great deal of pain and upset and distress and are not at all what people always WANT to do, even if they feel like they NEED to do them.