I think it's worth quickly considering the context of the poem.

It is addressed to two friends of his, Marcus Furius Bibaculus and Marcus Aurelius Cotta Maximus Messalinus, a poet and senator respectively. In Catullus-16 itself, it is referenced that both Furius and Aurelius believed Catullus' poetry to be rather effeminate. The exact word used is molliculi, which can be translated to 'tender', 'gentle', 'delicate', 'sensitive' etc. Taken at face value, the poem is a rebuke to the idea that Catullus himself is effeminate through threats of sexual violence against Furius and Aurelius. However, as these two were friends of his, and the poem is so atypical of Catullus' other poems, it is thought that the poem is supposed to be interpreted ironically, at least in part, and certainly has wider meaning. The point being made is that the poet does not necessarily match the poetry, and that crude poetry isn't as good as more 'sensitive' poems. Catullus-16 is complicated, but it is chiefly a rebuke to the idea that you can know someone through their public work. In the same way you do not know John Cleese by watching Monty Python, or Steve Coogan by watching Alan Partridge, you do not know Catullus by reading his poems. Inversely, Catullus is saying that even if he is masculine, that does not mean that his poems also have to be masculine.

So how was this message interpreted? It certainly seems to have stuck a chord with other Roman authors of the time. Ovid makes what appears to be the same argument in his own work, though more explicitly:

Believe me, my character’s other than my verse –

my life is modest, my Muse is playful –

and most of my work, deceptive and fictitious,

is more permissive than its author.

A book’s not evidence of a life, but a true impulse

bringing many things to delight the ear.

Or Accius would be cruel, Terence a reveller,

and those who sing of war belligerent.

Later on, he explicitly references Catullus as a further example of an author not matching the character of their work. Pliny the Younger sent some of his own poetry to his friend Paternus with the following message (from letter 4.14):

Some of them will possibly strike you as being rather wanton, but a man of your scholarship will bear in mind that the very greatest and gravest authors who have handled such subjects have not only dealt with lascivious themes, but have treated them in the plainest language. I have not done that, not because I have greater austerity than they--by no means, but because I am not quite so daring. Otherwise, I am aware that Catullus has laid down the best and truest regulations governing this style of poetry in his lines: "For it becomes a pious bard to be chaste himself, though there is no need for his verses to be so. Nay, if they are to have wit and charm, they must be voluptuous and not too modest."

Here Pliny is pre-empting a criticism he knows he will receive; that he does not imitate Catullus' lurid style even though the subject matter warrants it. Pliny explains that he does this because he struggles to be daring enough and is restrained by his own sheepishness. It also reveals that sexually explicit poetry really wasn't unusual in Roman society. Modern society may view sex as taboo, but the Romans (largely) did not. Pliny is expecting criticism not for too much explicit sexual content, but not enough. Pliny quotes Catullus-16 lines 5 to 8.

There is a lot of scholarly literature on the relationship between Martial's works and those of Catullus. Martial was, at the very least, a big fan of Catullus and imitated some of the sexual language used in Catullus-16.

The Roman author Apuleius, writer of The Golden Ass, was also a fan of Catullus. He was accused of using magic to seduce a wealthy woman, and his poetry (which often included magic) was used as evidence against him. He quoted Catullus-16 lines 5 and 6 in his defence:

You who are slanderous enough to include such charges in your indictment? For sportive effusions in verse are valueless as evidence of a poet's morals. Have you not read Catullus? "A virtuous poet must be chaste. Agreed. But for his verses there is no such need."

So overall, the poem would not have been controversial. It would have been a bit shocking, especially coming from Catullus, but that was the point and it worked. The poem deals with themes which were particularly pertinent to Roman writers and, going by how many subsequent poets used Catullus as an example, it was actually quite popular, and for many it was the go-to rebuke to people who thought they knew someone because they had read their work. We also have to consider that Romans did not have the same sense of taboo around sex that we do in modern times, and that sexually explicit poetry was not viewed as scandalous. The public response to the poem, at least from the evidence we have, is that people thought Catullus had a very good point.