Philosophy has always been about finding the truths of existence through logical contemplation. It was, it is, and it may remain so indefinitely. However, there is a problem when certain truths are excluded from the endeavor due to certain specifications. This leads to the creation of a hierarchy of truths, even though philosophy is all about finding the truth regardless of its category.
I personally find it surprising that such exclusion continues to exist even today, in a world where things can basically be divided into truth and falsehood. Everything that exists, therefore, is true, and everything that doesn't exist is either true in fiction or just false. There is no necessity to divide it and ignore certain portions of the truth. The purpose of philosophizing is to discover the truth, regardless of its type.
The principle I just mentioned about existence is also true when it comes to subjectivity. Subjectivity is not something that exists above existence in any way. Even when it comes to personal pursuits, for example, there are still some objective criteria by which something can be measured, and thus determined.
It is widely agreed by many, for example, that movies such as "The Room" are "Z-movies," or movies so bad that they have an actual category of their own. Thus, since Z-movies are real and "The Room" is an objectively bad movie, it would be truthful to conclude that it is a Z-movie, whether you enjoyed the movie or despised any second of it.
Subjective opinions are important, not because they are dear to the individual, but because they are not objects above reality. Philosophy is about discovering and spreading truth while avoiding falsehood. If subjective opinions are not completely false, then some of them must be true regardless of the emotional bias behind them, if such bias exists.
For example, if I think something is beautiful, and beauty is something to be measured through symmetry, size, color, and so on, then my opinion would probably be true as well, even though it is a product of my subjective experience.
There is importance in opinion even beyond philosophy. Otherwise, very few would actually care for it. When you give a testimonial for a business or an expert, that experience of yours is taken as proof of their expertise. It makes you assume that, if that expert received positive reviews, maybe they are an expert, as some have testified. Now, ask yourself: Is such a testimonial worthless just because it is subjective to the one who provided it? What if you used that expert's functionality and found out that said review was indeed true? If so, why discard subjective information that has proven to be correct, i.e., true?
By discarding a portion of the truth through exclusive specification, we not only do a disservice to philosophy but also prevent ourselves from becoming less ignorant about existence. Even when opposing subjectivities are involved, reality dictates that there is only truth or falsehood. It cannot be a hybrid. Such a thing is determined depending on the subject at hand and its appropriate measurements.
Another thing to remember is that truths don't have to be universal in order to be correct. The fact that it is correct for some and incorrect for others does not diminish its status as a truth. For example, it is true that apples are tasty. However, it does not imply that they are tasty to every human being, as different people have different tastes. It is "objective" that democracy is a good form of government, but that does not mean all would agree with this "objective" truth.
In addition, many "objective" truths are in fact subjective and are only seen as objective because they are widely agreed upon or even plausible. Do you think being 6'2" is tall? It is only considered such because it is a subjective impression to humans, but not to other beings, such as elephants, giraffes, and so on. If such animals could speak, would they blame us for pretending to be objective when they are far taller than us?
Thus, truth has two sides: universal truth and relative truth. The declaration of philosophy is to find the truth, regardless of what it might be. Wouldn't it be a bit hypocritical, then, to only seek one type of truth—one that might as well be more relative than one may think?
Much of our experience is dictated by our subjective inclinations. Someone has once called me a horrible writer, and yet, Quora has nominated me to be a Top Writer in the last year. As you see, the truth is out there, regardless of different experiences. Why, then, hold them in high regard as obstacles when they can simply be ignored in favor of the truth, which exists in either experience? After all, logic dictates that A and B cannot be one and the same. A horrible writer cannot be a top writer at the same time, can he?
In summary, experiences are valuable because they can contain fragments of truth or even reflect reality as a whole. They deserve to be questioned, like anything else, but subjectivity isn't the opposite of truth; falsehood is.