Merge conflicts are not so scary, and are an elegant way to handle distributed changes with simultaneous edits to a single file.
If the conflict is huge, rebasing can help you by "playing" the commits from one branch one at a time so the conflicts are smaller / easier to fix.
At a previous job, a team was forced to use checkout-style VCS due to their manager's unfounded fear of merge conflicts; I couldn't go in that office without hearing one developer shout to another: "Hey, can you finish up and check in that file so I can get started on my changes?"