Voting for someone who agrees with you 90 percent of the time is far superior to voting for someone who disagrees with you 100 percent of the time. This is exactly what will happen if people refuse to exercise their civic duty and boycott elections because they feel betrayed. Personally, I am not supportive of abortion at all, but I can support people who feel differently if, in the gigantic scheme of things, they can help put an end to the murder of innocent babies. This is especially true of those who are personally inclined to save and protect life.
Perhaps an illustration is in order: Two armies are engaged in a war. Let's call the good army that is trying to defend an entire society the red army and the bad army that is trying to invade and pillage society the blue army. The blue army occupies a superior strategic position and is composed of slightly more troops, putting the red army at a distinct disadvantage. Some in the red army feel that they are right and, therefore, should simply march directly into battle with the blue army because right always wins.
Fortunately, some members of the red army are wise and have a better plan. They send a battalion of troops to the base of the mountain occupied by the blue army to distract them while the vast majority of red troops approach the mountain from the backside. They descend upon the blue army by surprise, completely vanquishing them and winning the war. The decoy red battalion may have sustained some casualties, but in the long run, the war was won, and the entire society was saved.