The public's widespread belief in the existence of UFOs and their gene

Here is my take:

First of all, the public is an entity that takes a singular noun; this is a rule. For this reason, their or they should not be used to refer "public".
Further, use of their or they to refer to public complicates the situation because we have UFOs, which can be the referent of they or theirs.

Second, the public is in a possessive form, as in "public's wide spread interest". A pronoun such as its can refer to a referent in a possessive form.
For example, Tom's toy is cool; his is better than mine. This is completely fine.

Where it becomes problematic is when the pronoun is used as anything other than a possessive form.
For instance, Tom's toy is cool; he paid more than I did. In this case, he has no referent because Tom's is just a noun modifier in a possessive form.

Last but not least, "and" form a compound subject that requires plural verbs: when two subjects publics's wide BELIEF and their general CURIOSITY, the sentence calls for HAVE
However, "as well" as is a coordinating conjunction. A coordinating conjunction calls for a singular verb to fulfill the agreement requirement.

I do, however, have some doubts about correctness of the answer choice.
I strongly think that there should not be a comma before the verb has because a comma is not allowed between a subject and a verb in grammar.
I think the sentence would have been more flawless had the comma not been there or had another comma was placed before as well as.
For example, the sentence would look like: The public's widespread belief in the existence of UFOs, as well as its general curiosity about extraterrestrial life, has generated considerable interest in science fiction