What the lingam signifies is genuinely disputed, and the dispute is old, internal to Hinduism, and then badly aggravated from outside.
The Sanskrit word linga means a mark or a sign, in logic, the evidence from which something is inferred. A substantial body of Shaiva theology takes the object in exactly that sense: the formless Shiva has no image, and the lingam is the sign of that formlessness rather than a depiction of anything. Many practitioners hold this position firmly and reject the anatomical reading outright.
Other texts within the tradition, including parts of the Puranic literature and some tantric material, treat the phallic reading as intended and theologically meaningful, and pair it deliberately with the yoni base as the union from which the world proceeds. This is not a scandalous reading smuggled in from outside; it is inside the corpus.
What happened from outside is a third thing. Nineteenth-century European scholarship and missionary writing seized on the second reading and presented it in a register of prurience and disgust, as evidence of a degraded religion. That framing was intended to demean and did. Hindu writers have been objecting to it since, and modern controversies over how the lingam is discussed in Western textbooks and scholarship are continuous with that history rather than separate from it.
The result is that a question with two defensible answers inside the tradition became, from outside, an accusation. Anyone writing about the object now is writing into that, and pretending otherwise is not neutrality.