I'm sure I'll get this wrong, but the way it was explained to me is that you need to appear in 3 SAG productions in order to apply for membership. Since it's a big hassle for the movie production to get an exemption to hire non-union, you need to be special in some way (the director really wants you in particular, you have some special skill like dance, etc.). It helps to know other actors who will call you and say "hey, they need a ballerina to be in the background tomorrow" or whatever.

I'm also not sure how you'd bootstrap something like this for programmers. The reason it works for actors is that every actor who is even slightly famous is a member, so every production has to work with the union or only get completely random people (you're still allowed to make an indie film with your friends if none of them are members).

I think the selectivity problem is less of one for programmers than screen actors. We can use code tests or Github for membership screening. Thus, we don't create the chicken-egg problem where (a) it's almost impossible to prove yourself if you're not part of the union while (b) you have to prove yourself before you can join.

Getting broad-based membership is much harder. This is an industry full of (a) young people who think they'll have investor contact in 6 months and be founders in two years and retired in six, and (b) indentured servants on H1-Bs. Even if we get 95% of the top 50% of programmers (and that's wildly optimistic) as members, most managers will just ignore their need for talent, in that case, and hire bottom-rung engineers, preferring that over being responsible for bringing in a union. It (that is, hiring bad engineers to avoid bringing in represented ones) won't work, but it won't hurt those managers' careers personally, so nothing will be done about it.