All the items posted in 43 are in the realm of sins or potentially sinful – alhtough many of them revolve around speculation and rumor, and no, the Church does not persecute or punish based on rumor.
The “couple” (self-defined) was not being kicked out because of sin, or assumed sin. The “couple” was denied a position in the school as dual heads of family because of the visibility of their fundamentally oppositional description of family, since the family unit is at the heart of every Catholic school. Had the child been merely presented by one woman, who described herself as a single mother (for example, unmarried mother), her lifestyle could have been anything as long as it was not public. It is the public nature of it that creates the scandal. The whole community could gossip about that single mother (“Is she living with someone?” "Is she divorced but considering remarriage without annulment? “Is she a lesbian?”), but there is not really a controversial issue unless that woman were to make it a controversial issue. So if she brought her lesbian lover to the first parent-teacher conference in kindergarten, yes, that would become an issue. If she brought her live-in boyfriend to those meetings, and publicly declared he was her lover, that would, like this case, become a scandal, and the school would be within its rights to disenroll the child next year because of the problem of scandal.
This case is more publiciized, but I’ve seen all kinds of different scandalous situations (again, with public flaunting of a lifestyle, some of which are named in post 43) become reasons for not enrolling a kindergartner in the first place, and/or not continuing the enrollment the following year.
There is a component to Catholic education that does include being a practicing, faithful member of the parish, in good standing. Most school administrators are not going to check every nook and cranny, but spaces in very desirable Catholic schools, in desirable locations, are limited, and there is wide discretion and a kind of prioritizing of who gets admitted. Understand that it works to the benefit, also, of those who are truly in a situation which in its very nature, calls for compassion, such as recently widowed single mothers, or those who appear to be living a wholesome lifestyle and have encountered a tragedy of which they are truly a victim (natural disaster, etc.)