I would like to make a more general contribution, but still regarding your specific question.
There are many definitions of synonymy. Let's agree in a simple one: it is a semantic relation between the meanings of words or sentences. We now have the problem of defining "meaning". In one way or another, the concept of synonymy is uderstood without requiring absolute identity between words, if there is such thing. Without going in the details, a logical account for absolute synonymy would say that two linguistic forms are synonyms if they are interchangeable salva veritate, that is, keeping the truth value of the expression they are part of. In his attack on the concept of analyticity, Quine (1951) discussed the idea of whether this kind of interchangeability was a condition strong enough for synonymy. Saying that
bachelor is a synonym of
unmarried man was saying that the proposition all and only bachelors were unmarried man was analytical. But that is circular, and Quine wanted to discuss whether the sufficient condition for cognitive synonymy was interchangeability and not analyticity. Hundreds of articles have been written about this and I cannot review all the arguments, but the point was to illustrate one of the basic ideas about logical synonymy. If you think about the example of the correspondence between
unmarried man, you will soon realise that there are not really many words like those in natural language.
So, if we talk about words, we think that synonyms are those that can be substituted for each other in sentential contexts, and if we talk about sentences, then they are said to be synonyms if the substitution preserves truth values. But still we have to be careful with the concept of synonymy. For words, we can have different semantic values that may not have a one-to-one correspondence to each other. Think about the words
old, ancient, aged, obsolete. They are not interchangeable in all contexts:
old/ancient ritual vs.
old/?ancient laptop. So it's not only about the meaning of the synonyms, which is unclear, but also about their relations with other words on their contexts of appearance (the basic idea behing compositionality in semantics). We can also use euphemisms as synonyms for the words we don't want to use. Here we are opepning the door to a whole new set of factors that can influence synonymy, as some previous comments/answers point out. We must then consider that synonymy (either absolute or partial) depends on what are the meanings we are trying to compare and the compositional nature of the relations between words in the context of sentences. This is a matter of debate for any kind of approach to meaning, either in semantics, pragmatics and other subfield.
Let us admit that there can be at least two kinds of synonymy: there might be a full synonymy for words that are logically (salva veritate) interchangeable, but that is not very common. And there is also this everyday use of synonymy that treats sameness of meaning in a more or less unrestricted way. One could see meaning as some sort of continuum and words as mapping certain parts of that continuum, with overlaps between them that allows us to call them synonyms. This can be analysed theoretically and empirically in linguistics. As was mentioned before, definitions depend on the framework used to explain meaning. If the meanings of words are their referents, then it is easy to find synonyms. A second option is to understand that meanings are senses (more or less in he Fregean conception), but then you will find many debates as well. A third option is a psychological perspective were meanings are representations or concepts in the mind, and there you will find even more disagreement. The definition of synonymy is then closely related to the semantic perspective adopted and the definition of meaning endorsed. You can compare words in terms of denotations, semantic features, semantic maps, representations, etc. You can also study synonymy in terms of sociolinguistics, comparing dialects and registers, or even from a cross-linguistic point of view. The use of computational methods and corpus research is also frequent. But at the end, you can only say that there is absolute synonymy if you analyse all the possible meanings/contexts, and that is quite difficult, if not implausible.
In sum, definitions of synonymy are relative to the theoretical framework adopted, and particularly dependent on the definition of meaning. What you call "absolute synonymy" can also be what has been defined as logical or full synonymy, but not everyone will agree. Words like
unmarried man can be said to be full synonyms, but then again, these examples are extremely rare and there might be differences we don't know yet. That is also the case of
furze, mentioned in a previous answer. Perhaps the reason is that these words have a very narrow range of contexts of use. It might be the case that words with more meanings and more frequently used tend to be less close to the end of the continuum where full synonymy (if it exists) is found. Besides, two or more words that mean exactly the same seem to be not economical for language, and thus it would tend to be avoided. Are there absolute synonyms? There can be, but then again, the answer itself is not absolute. I am sorry I can't provide references, but it seems that's the situation, at least in linguistic semantics. Partial synonymy is assumed for methodological purposes without much discussion, while absolute synonymy is considered rare because it is inefficient and uneconomical.