Lots of people would feel anger and resentment, especially against the Catholic Church, too many to just ignore. That’s the case now anyway. And Jesus said his Church would be hated.

(Better let the media handle something like this.)Yoy! They’d handle it alright. In my mind I see them fanning any spark of discontent into flame. I suppose there is “good media” too, which is probably what you meant.
And what if abortion worldwide would suddenly come to an end? What chaos would ensue?
The chaos came first and is going ON. Abortion is terrible. Not a good thing at all. On another front (while I have thoroughly enjoyed imagining that happy moment you’ve painted Robert Sock), cynical me thinks it probably won’t happen til the end of the world - and that THAT chaos will absorb many people and make them think about abortion less and less - and their eternal fate more and more.
Social change like this takes planning. especially when the social pendulum is swinging in favor of abortions and women’s rights. It’s good to plan for the most part. But when lives are in danger committee meetings become less prudent and could border on the idiotic. The babies saved would be worth the social unrest! Not to go wishing for social unrest of course.
This very sensible sounding statement could be (worst case) a justification to do nothing (or postpone the good we can do now) as a compromise with evil. It’s a little bit “Pontius Pilate” or too clever for its own good.
“Peace” is good for example - but “submitting to slavery” rather than fight in the name of peace is an error. It’s easier to rationalize compromises with evil when we ourselves are not the beneficiaries of moral stand.
You may be right about what might happen. But it should not dampen our desire for a just society and its fruits.
A society where young women take pride in being life givers - and not equal pride in being life takers – is a big step forward. A pregnant woman is a treasure chest - not a garbage can. And Doctors should heal and never destroy for a bribe.
There would be side effects as you point out - but if a society was good enough to wash the stink of abortion from itself - it would equally find ways to help women (and babies and men) in dire circumstances too. And it probably would not cop out to violence, selfishness, greed and destruction, either.
Let those Church bells ring! Babies are wonderful!
http://t1.gstatic.com/images?q=tbn:ANd9GcTHMKFBsvRGKlPzMyT2cbQBb7SeWCO3rhtJdeiA1yrF9lsk0q5- – not born yet in this picture … but a person as you can see. A person who might be saved if “abortions suddenly became illegal.” The suddenness would be " just sudden enough" to save some. Because many people would NOT pursue illegal abortions.

Some still would of course.
. .