Here is a link to a good article by Richard Doerflinger on the Equality Act and abortion. Here is his conclusion:
The “abortion as health care” campaign advanced by the Equality Act effectively defines the unborn child out of existence. It treats the child as merely a “physical condition” of the mother that health professionals are called on to address through corrective treatment. In a sense the Act also defines Americans who object to such taking of innocent human life out of existence as well, treating them as bigots who must be forced to comply with anti-discrimination policies accepted by all fair-minded citizens. The Act does not promote equality, as it further demeans vulnerable human beings who already have few rights — and denies the right of pro-life Americans, who make up about half the U.S. population, to live by their fundamental convictions. In no way should its enactment be the goal of a “presidency for all Americans.”