It seems to me that a disagreement among rabbis can very well acquire the status of a safek.
The Gemara in Avodah Zarah (7a) says:
היו שנים אחד מטמא ואחד מטהר אחד אוסר ואחד מתיר אם היה אחד מהם גדול
מחבירו בחכמה ובמנין הלך אחריו ואם לאו הלך אחר המחמיר ר' יהושע בן קרחה
אומר בשל תורה הלך אחר המחמיר בשל סופרים הלך אחר המיקל א"ר יוסף הלכתא
כרבי יהושע בן קרחה
If there are two sages present and one declares unclean and the other
clean; one forbids and the other permits; if one of them is superior
to the other in wisdom and in numbers, his opinion should be followed.
Otherwise, the one holding the stricter view should be followed. R.
Joshua ben Korcha says: In laws of the Torah, follow the stricter
view. In those of the rabbis, follow the more lenient view. Said R.
Joseph, the Halacha is according to R. Joshua ben Korcha.
The Rambam (Mamrim 1:5) rules this way as well, and incidentally this is the same way we rule on every matter of safek; i.e. in questions of biblical law we are strict and in questions of rabbinic law we are lenient. To me, the simplest explanation is that these two rulings are one and the same, for every matter of doubt based on conflicting opinions is actually a safek.
However, there are certain considerations one needs to take into account. Most basically, everyone has the right to an educated opinion. If someone is confident about their opinion and has the requisite knowledge to be this confident then it is certainly not Halachically considered a safek to them, regardless of who disagrees, as long as this opinion works within the Halachic system. For this reason the Rambam (ibid) qualifies the above ruling by saying it only applies "when you do not know which way the law leans." This is why the Shulchan Aruch will often rule in accordance with one opinion and not the other without mentioning that it is a matter of doubt, because to him it simply wasn’t. He ruled that way because in his opinion that view carried more weight logically.
A spinoff of this consideration is the fact that everyone has the right to have a specific rabbi one always follows when one does not know the Halacha. The Gemara’s ruling is only to prevent picking and choosing in a Halachically arbitrary fashion, but one who says “I always follow Rabbi X” can follow him even when he is a lenient minority and it is a question of biblical law. As the Gemara itself (Eruvin 6b) says:
והרוצה לעשות כדברי בית שמאי עושה, כדברי בית הלל עושה, מקולי ב"ש ומקולי
ב"ה רשע, מחומרי ב"ש ומחומרי ב"ה עליו הכתוב אומר (קהלת ב:יד) הכסיל בחשך
הולך, אלא אי כב"ש כקוליהון וכחומריהון, אי כב"ה כקוליהון וכחומריהון
One who wishes to follow the words of the House of Shammai may do so.
The words of the House of Hillel; may do so. The leniencies of the
House of Shammai and the leniencies of the House of Hillel; is wicked.
The stringencies of the House of Shammai and the stringencies of the
House of Hillel; upon him Scripture (Ecc. 2:14) says “the fool walks
in darkness.” Rather either the House of Shammai with their leniencies
and their stringencies, or the House of Hillel with their leniencies
and their stringencies.
As the Gemara elaborates, the specific application mentioned in the passage does not apply anymore; for reasons not relevant to this discussion.
The point is that one does have the right to choose an opinion even though one is not sufficiently educated and knowledgeable to have one, as long as one always follows the opinions of this individual and is therefore not acting recklessly and wickedly.
On this authority we can theoretically follow the decisions of the Shulchan Aruch even when we do not feel confident enough deciding ourselves which of the Rishonim got it right. The idea is, simply put: the Shulchan Aruch is our rabbi. When we don’t know, we always follow him. Or the Rema. Or the Aruch HaShulchan. Or the Mishna Berura. This can apply to anyone, and is really the concept known as posek acharon, final Halachic authority. It isn’t that we truly believe that any particular person has the final word, but there are certain people we hang our hats on, so to speak, in all cases where we aren’t confident to have our own opinion. Doing so is of great benefit to us for this very reason – it takes care of a lot of doubts and precludes them from acquiring safek status.
In summary: Every disagreement is potentially a safek, but in actuality if one has a confident, educated opinion, or if one consistently relies on someone else who has a confident, educated opinion, then said opinion does not have the status of safek at all (unless one has an educated, reasonable doubt about the particular opinion that is not simply translated as "but someone else said...").