It is often claimed that if we enforce some policy or allow some behavior; then it will not stop there but further policies and behaviours in that direction will be enforced or allowed until some undesirable end point is reached.
i.e. Once we step onto a slippery slope, we will slide to the bottom.
When does this apply, and when does it not?
It does not apply when there is a qualitative distinction which prevents further sliding.
Nepotism, or favouring family over strangers, is not the first step on a slippery slope to favouring everybody exept oneself - nepotism gets weaker (and other incentives get stronger) with reducing degrees of relatedness.
(Favouring strangers over family is a slippery slope.)
Eating animals for food is not a slippery slope on the path to eating people for food.
(Moral vegetarianism is a slippery slope.)
But there are real slippery slopes, and these occur when there is a violation of a qualitative distinction; because once the qualitative distinction is violated then there are only gradual, incremental, quantitative non-distinctions preventing descent of the slippery slope.
There are many examples from the past decades and few centuries in relation to leftism/ progressive/ Liberal politics.
When a qualitative distinction between men and women is denied, then there is a slippery slope.
When the qualitative superiority and sanctity of heterosexual sex and marriage is denied, there is a slippery slope.
And so on.
The point is that it is relatively predictable; we pretty much know in advance when one is stepping onto a slippery slope, and when one is not.
When one is violating a natural taboo, or a religious taboo; or violating natural law or revelation, then a slippery slope has been stepped onto.
No matter how small the step - once onto the slope, the slide downward will begin (slowed only by the inertia of persons and society).