How do I decide whether I should spell the word "idolator" or "idolater"?

Both spelling are accepted, but idolater is the more common. The suffix -or is typical of terms of Latin origin while the suffix -er with terms of German origin. But there are several exceptions as shown below, and "idolater" appears to be one of those:

Idolater (n.):

• late 14c., ydolatrer "idol-worshipper," from Old French idolatre, contracted from Late Latin idololatres, from Ecclesiastical Greek eidololatres "idol-worshipper."

-er:

• English agent noun ending, corresponding to Latin -or. In native words it represents Old English -ere (Old Northumbrian also -are) "man who has to do with."

• Generally used with native Germanic words. In words of Latin origin, verbs derived from past participle stems of Latin ones (including most verbs in -ate) usually take the Latin ending -or, as do Latin verbs that passed through French (such as governor); but there are many exceptions (eraser, laborer, promoter, deserter; sailor, bachelor), some of which were conformed from Latin to English in late Middle English.

(Online Etymology Dictionary)

Well, if they really are both considered acceptable (it seems to be the case, at least according to several reputable English dictionaries), I'd go with the most frequently used word. A quick check with Google ngram shows that idolater comes up about five times more often than idolator:

Perhaps you should use the most common spelling, which is "idolater"; as both spellings are regarded as acceptable, you are not constrained to do that, although it's probable that more of your readers will consider "idolator" to be unacceptable than will object to "idolater" so that if audience reaction is your concern "idolater" is better. Historically, the Middle English forms were "ydolatrour" and "ydolatrer" which became "ydolatour" and "idolater" in early modern English. The "idolator" form may be a 17th century form introduced by some scholar who thought the Latin "or" was appropriate although the word came into middle English not directly from Latin but indirectly through French (which used "re" not "or"). So if historical authenticity is your concern it seems again that you should probably choose "idolater".