Surrendering oneself to Allah through tawḥīd is to single Him—glorified and exalted—out in worship. This is the very meaning of tawḥīd: whoever worships Allah alone, without partner, has truly submitted to Him.
As for the phrase, “and to submit to Him through obedience,” it means complying with everything He commands and refraining from everything He forbids. Whatever He enjoins, you carry out; whatever He prohibits, you avoid—out of obedience to Allah.
The words, “and to repudiate shirk and its adherents,” indicate that barāʾah (disavowal) entails severing, distancing, and separating oneself from idolatry and from those who practice it. You must believe that shirk is false, stay far from it, and hold that enmity toward the polytheists is obligatory, for they are the enemies of Allah. Therefore do not take them as allies; regard them instead as foes, for they oppose Allah, His Messenger, and His religion. Do not love them or side with them. Rather, cut off relations with them in matters of faith, keep your distance, and affirm the falsity of what they follow. Show them no affection in your heart, and do not support them by word or deed, for they are enemies of your Lord and your religion. How, then, could you ally with them when they are enemies of Islam?!
It is not enough to surrender to Allah and obey Him while failing to renounce shirk and the polytheists. That will never suffice, and you will not be counted a Muslim until you possess all of these qualities.