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I cannot speak about the Renaissance, but I do know a bit of Plato. So I'll give you some background on Plato's thought (and some relevant sources) and hopefully someone else can chime in with some insight into Plato's influence during the Renaissance.

To understand Plato's views on art, we have to understand something of his general epistemology and metaphysics.

Plato put forward the theory of forms. Roughly, this means that the "highest" level of reality is purely abstract, intelligible forms that the particulars we experience participate in. So, when I say something like "That action was good", Plato takes this to mean something like "That action participated in the form of the good". The visible world of particulars, i.e. chairs and computers and all that, is less "good" than the world of forms. The proper objects of contemplation and the true nature of reality are the forms, of which observable "everyday" reality is a mere shadow. This is a major upshot of the allegories of the sun, line, and cave, for instance.^1

Now, I don't want to go too deep into the philosophical rabbit hole here. The main upshot is that Plato thinks that what we should focus on is the world of abstract forms, not the world of concrete objects and sensations. The most important such form is the form of the good. Interestingly, Plato sometimes talks as though the form of the beautiful is intimately connected in some way to the form of the good,^2 making an analysis of beauty a central tenet of his thought.

So, with this knowledge in hand, what can we surmise about Plato's views on the visual arts and individualism? Well, if the point of human thought is to try and approach the forms, we shouldn't care much about the individual bit of art we encounter via sensation. Of course, sometimes such a bit of art might help us get started down the path to thinking about the forms, but even so they are just a means to an end. At best, then, a bit of art will participate in the form of beauty and set our minds on the path to contemplation of that form. At worst, a bit of art will just distract us. Plato appears to be of the opinion that the latter is more common. And, in any event, once we reach a decent level of intellectual sophistication we won't want to think about a specific paintings (or whatever) anyway, since we will just be contemplating the form itself.

The all encompassing importance of the form of beauty also naturally tells against individualism. To be beautiful is just to participate in the form of beauty; individuals can add nothing to this perfect ideal form. To the extent that the artist is individualistic, then, the art becomes less valuable/beautiful. The universal form of beauty is all that matters, not the particular viewpoints or perspective of the artist.

Sources

1. For the relevant passages of Plato, see Republic Books 6 and 7. For some analysis and summarizing comments by professional philosophers, see the SEP and sources cited therein.

2. Hippias Major, 296d.

3. For a more general overview of Plato's aesthetics, see this article.