The dramatic schism that opened up between Corporate America and President Donald Trump this week might look like an outlier, of reputational risk coming to outweigh any benefit business hoped to get from forging a good relationship with an administration that could help them on tax and regulatory policy.

But it isn’t an outlier, and to understand why, look to Austin, Texas, not Washington, D.C. There, a seven-month effort by social conservatives, backed by Republican Gov. Greg Abbott, to regulate transgender access to public...