Its ubiquity makes it a flashpoint, and the objection is theological and specific rather than general.
Salafi and Wahhabi criticism focuses on particular verses, above all those addressing the Prophet directly with requests, and those attributing to him a role in the created order. The line most often cited as objectionable says that of the poet's generosity is this world and its rival the hereafter, and of his knowledge is the knowledge of the tablet and the pen. Critics read this as attributing to a human being what belongs to God alone, which falls under shirk, association, the one thing Islamic theology treats as unforgivable.
Defenders argue that the language is the conventional hyperbole of Arabic panegyric, that the poet elsewhere states plainly that the Prophet's excellence has a limit and that he is a human being, and that the verses in question are intercessory rather than worshipful. Classical commentators, including entirely orthodox ones, addressed the issue and defended the poem, and it has been endorsed by scholars of every Sunni school.
The dispute is therefore internal to Sunni Islam and old, and it intensified with the rise of Salafi movements in the modern period. In some countries the poem is a routine part of public religious life; in others its public recitation is discouraged or forbidden.
An account that presents it as uncontroversially beloved misses half the picture, and one that presents it as heterodox misses the other half. It is beloved and it is contested, by different Muslims, on stated grounds.