"Causing others to stumble" means to cause a fellow Christian to do something he/she considers wrong. It does not mean doing something someone else thinks (or is convinced) is wrong. First Corinthians 8 addresses not causing others to stumble regarding the conviction of eating food sacrificed to idols. For some, eating food offered to idols was a sin because they always associated that food with worship of idols. Paul commanded those who could, in good conscience, eat food sacrificed to idols (viewing it merely as food) to refrain from eating it so others would not be stumbled. Romans 14:13–23 also addresses not causing others to stumble based on what they eat. Instead, believers are to love one another, hold onto our convictions, and pursue “what makes for peace and for mutual upbuilding” (Romans 14:19).
In the western world, we generally do not have the problem of food offered to idols. So to use a different example, let's look at drinking alcoholic beverages. There are many Christians who are convinced that it is wrong for them to drink alcoholic beverages. However, Scripture does not speak against drinking alcoholic beverages; it speaks against drunkenness (Ephesians 5:18). So if a Christian looks at the Scripture, realizes that drinking alcoholic beverages is allowed, and therefore enjoys a beer or a glass of wine occasionally, he/she is all right with God to do so. However, suppose that Christian, who is free to drink alcoholic beverages in moderation, invites another Christian who is not free to enjoy alcoholic beverages for dinner. If the first Christian, knowing of his/her invitee's lack of freedom, then has a beer with dinner and gives one to his/her guest, he/she is encouraging the invitee to do something he/she considers to be wrong. If the invitee takes and drinks the beer, he/she has then gone against his/her conscience, and the host has caused the invitee to stumble. A much better approach for the host would be to forego the pleasure of the beer and have no alcoholic drinks available at dinner. For the host to cause the invitee to do what he/she considers sin is for the host to sin.