I think it falls under the first amendment as well - and think a case needs to be made in that vein and pretty sharpish by a legal eagle. There has been quite a lot of faff and liberals dropped the ball on this one.
I'm less concerned about same-sex and interracial marriage and contraception. I think these are on slightly more solid ground and Alito does seem to have suggested he thinks abortion is a special case because of the life question.
I think if they push it further into an ideological side-picking contest, the Republican vote will not recover for a few generations. There are moderate sensible and centre ground republicans (not that you'd believe it if you read faux-liberal writers on Medium)