1)I still see discrimination based on existence of bikini-level pictures online problematic. I am not denying it is happening, but I'm not sure many companies actually write it down into their policies, as it can be very easily sexist.
As a bonus it is totally subjective and random (whose photos are found).
It's not just inappropriate images, it's anything posted on social media that is considered inappropriate and incompatible with an organisations core values and image. In the education sector 'safer recruitment' practices mean that some schools are checking social media as part of the recruitment process. They're not just trying to search for pictures but also anything else that could make you unsuitable to work with children or bring the school/profession into disrepute.
I've worked in Careers and Employability and have seen candidate's being removed from a recruitment and selection process because of something posted on social media. It happens fairly regularly. Quite often it's about the image of the organisation.
2)it isn't hiring managers who do the checks. It is HR specialists, assistants. If they don't see it as a big deal themselves and no written policy exists, the hiring manager doesn't have to know.
Depends of the sector. I'm currently involved in a huge piece of research on this and I'm speaking literally to hundreds of employers across a range of sectors and it varies. In some places HR have minimal involvement in others they do everything.
However, a policy is likely to exist. It might not specifically refer to inappropriate pictures but it will talk about professional image or behaviour that has the potential to bring an organisation in disrepute.
3)Z and alpha are huge numbers altogether and more and more relevant on the job market. World is already getting used to them.
I don't disagree that the world is changing and in 10-15 years we might see different results and views on this but at the moment Z and Alpha are entering the labour market, they generally aren't in positions where they are hiring people. For Z' s and Alpha's this behaviour is so normalised but that isn't the same for older generations who are typically responsible for employing people.
Some sectors are already more accepting but there are some where this will never be the case I suspect ( Education, Law, Health)