However you swing it, the kitty's a Beckett and change.
And you can count yourself lucky that they are writers, so you only got dropped from the industry.
To our international friends: be very careful of your agencies, and always read the papers they provide.
They're not going to hold to the US for their scabbing desires.
No, this isn't how this works. It would be crossing the line if you were taking an otherwise union job or the workers had asked for a boycott. They have not. There are legitimate strategic reasons for this, most unions do not ask for boycotts during strikes, since this increases pressure on the bosses.
https://mashable.com/article/sag-aftra-wga-strike-what-counts-as-crossing-picket-line