Here is what I think is a valid argument:
(P1) There exist instances where civil disobedience (i.e., disobedience of laws and even minimal violence) may be legitimate to correct grave injustice.
(P2) If there exist any instances where civil disobedience may be legitimate to correct grave injustice, then state-sanctioned mass murder is such an instance.
(P3) Murder is the deliberate killing of an innocent person.
(P4) If the unborn are innocent persons, then abortion is state-sanctioned mass murder.
(P5) The unborn are innocent persons.
(C) Therefore civil disobedience may be legitimate in cases of abortion.
The question of whether abortion should be legal is precisely a question about (P5): if the pro-life camp is correct, then abortion just is the state-sanctioned murder en masse of unborn human beings. What I therefore find somewhat strange is the idea that the abortion debate should purely be a civil debate (i.e., a debate where both parties argue their case before the body politic and accept its judgements without recourse to any extra-legal methods of achieving one’s ends). But if someone accepts (P1)–(P4), then the correctness of the pro-life position would necessarily entail that individuals are not bound to submit to the diktats of the body politic and are entitled to use extra-legal methods to prevent abortion. In other words, it is not coherent for a pro-lifer to think that a “civil debate” (as defined above) on abortion is even coherent: if the pro-life position is amenable to civil debate, then it cannot be correct. Symmetrically, a pro-choicer cannot think that a “civil debate” is coherent: if they are unwilling to grant the possibility that their opponents could be legitimate in using civil disobedience to achieve their ends, then they are unable to grant the possibility of their opponent’s arguments at all. Both of these conclusions follow necessarily, unless one abandons at least one of (P1)–(P4).
The problem is that (P1)–(P4) are simply not controversial. It seems that almost nobody will want to say that North Korean dissidents, e.g., are acting illegitimately, which gives us (P1); (P2) seems likewise trivially obvious (do we really want to argue, e.g., that a dissident North Korean family that helps the to-be-executed to flee to South Korea are acting illegitimately?); (P3) seems likewise non-controversial unless one is going to tie oneself in contortions; and (P4) is analytic on (P3) given that abortion laws simply are the state’s sanctioning of abortion and given that abortion occurs at a large scale (depending on the country, generally at least in the thousands or tens of thousands per year in places like Australia, up to 850,000 in places like the United States ).
So, to insist that the legality of abortion be decided by civil debate (as defined above) is then seemingly precisely to insist that the legality of abortion need not be decided at all, since (P5) could not be true if abortion was able to be decided by civil debate.
To be clear, nothing in my argument above would indicate that civil disobedience is morally obligatory in respect of abortion, nor that pro-life advocates should not argue their case before the body politic. It is simply to argue that pro-life advocates cannot coherently advocate that abortion is wrong while also arguing that it is necessarily illegitimate to commit any acts of civil disobedience in defence of the unborn.
 “Induced Abortion in the United States”, Guttmacher Institute, https://www.guttmacher.org/sites/default/files/factsheet/fb_induced_abortion.pdf.