"Behead" or "beheads"?
Parallel structure between the two options requires beheads. Both verbs need third person, singular, present form.
Which is true? 1) Hamas drives Christians out of Gaza; or 2) Hamas beheads them [Christians]?
Part of the problem is the distinction between the factual and counterfactual. Most negations do not use a simple present form, but use helping verbs instead
He goes to school. She does not go to school.
The speaker is stating Hamas drives ... but also Hamas does not behead ....Instead of using the does not construction, he uses the conjunction rather than to negate. As Merriam-Webster indicates, *rather than can take either infinitive forms or parallel conjugated forms.
- — used with the infinitive form of a verb to indicate negation as a contrary choice or wish: chose to sing rather than play violin
- and not: obscures rather than resolves the problem
If you wanted to rephrase because it sounds a bit off, you could say
Hamas only drives Christians out of Gaza but does not behead them.
Note that the verb form does in this alternative is the third person singular, present, parallel to drives.
Another alternative is
Hamas only drives Christians out of Gaza rather than beheading them.
No, behead is not acceptable in that particular instance; it would be a singular rather than a plural. Whether 'Hamas' should be treated as a collection of individuals, who do something or as a group which does something is a fruitful source of argument; there are several questions already on this site. However, if you have already said that Hamas drives people out, the corresponding word is beheads.
The confusion may come from the many constructions possible in the context, and only slightly different. The subjunctive would be It has been suggested that the group drive the people out [next Sunday] as opposed to It has been suggested that the group drives people out [but I haven't seen it myself]. Another possibility would be the gerund, ...rather than beheading them. But as written it is a simple present, which means the ending depends on number.