John Chrysostom

"Let us go forth therefore to Him without the camp, bearing His reproach," that is, suffering the same things; having communion with Him in His sufferings. He was crucified without as a condemned person: neither let us then be ashamed to "go forth out" of the world.

Homily on Hebrews 33 ↗

Theophylact of Ohrid

Since Jesus Christ suffered outside the gates, let us also go out to Him outside the gates, that is, let us be outside the world, "bearing His reproach," enduring the same sufferings. He, as one condemned and a robber, was crucified outside; let us also not be ashamed to withdraw from the world and from its luxury, even if this should seem dishonorable. Again he persuades them to endure the insults inflicted on them by the Jews, or the plundering.

Commentary on Hebrews ↗

Oecumenius

"Let us then go to him outside." Since Christ suffered outside the gate, let us go out to Him outside the camp, that is, outside the world, bearing nothing worldly, neither earthly nor carrying the filth of the earth. This, outside the gate, that is, outside the world, bearing His reproach, that is, suffering the same things as He did, if He should ask; for this indicates, bearing the reproach he endured, which He Himself endured through both the mockeries and the scorn.

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

Then when he says, Therefore let us go forth to him, he draws two conclusions. In regard to the first he says: Therefore, we have said that we have an altar outside the camp. Hence, we must do two things: namely, go to it and sacrifice upon it. He tells how to go when he says that Jesus Christ suffered and bore the reproach of His passion outside the gate; therefore, let us go forth to him outside the camp, i.e., outside the general community of carnal things, or outside the observances of the Law, or outside the senses of the body, …

Commentary on Hebrews ↗