No. Most current grammarians and most style guides do not say that split infinitives are prohibited. Furthermore, in the past when some grammarians said they were not allowed, that were as many or more equally authoritative grammarians who said there was no such rule, and those who did support such a rule never were able to offer a good reason for it.
The only reason one may want to avoid them now is that there were still enough people who were taught from crappy elementary school textbooks that had this bogus rule, and they will think your grammar is bad if you use split infinitives (and they remember enough from elementary school to recognize them).
Just trust your ear. If splitting an infinitive makes a sentence sound clearer, do it.
If someone gives you crap, cite the Oxford Dictionary people [1].
PS: same goes for ending a sentence with a preposition. Sometimes it is clearer to do so. In that case, do it! You can cite Oxford for this, too [2].
And the silly thing is that the rule was based on Latin, where to infinitive is marked by a (non-separable) suffix, as opposed to English where it's marked by a preposed preposition "to" (though that may be redundantly put).
