Remembering the emotions
Descartes never says that we are merely cognitive beings. Thinking may be our essence - may define our essential nature - but we are also creatures of emotion or 'passion' as the term is usually rendered in translation.
In the Passions of the Soul he identifies six primitive passions :
The first primitive passion is  wonder, which occurs when an unfamiliar
object is encountered and which "we . . . find novel, or very different from
what we formerly knew or from what we supposed it ought to be . . . ."
Wonder is first and foremost because it occurs before the object has been
determined to be "beneficial"; and it has no opposite, since looking at an
object without wonder is to look at it "without passion."
Descartes in fact defines each of the primitive passions through a differentiation which occurs on the biological level through the movement
of animal spirits. Wonder, however, exhibits no such movement, while
each of the remaining primitives does. Though it may sound strange to
speak of animal spirits as the determining ground for passions, it is not
so far removed from our modern account of hormonal disposition.
The second and third primitives are those of  love and  hate. In the first
definition, love for something is simply the thought that this thing is
good [beneficent]; and hate, that it is harmful. Following these two is a
pair:  joy and  sadness. "Consideration of a present good arouses joy in us,
and consideration of a present evil arouses sadness, when the good or
evil is one that we regard as belonging to us."
The final primitive is  desire. Like wonder, desire has no opposite and is always directed towards the future. It disposes "the soul to wish, in
the future, for the things it represents to itself as agreeable." Desire
pertains not only to the want of good in the future, but also the "preservation" of good which exists in the present. Descartes does not pair aversion with desire on the primitive level. Aversion is simply the desire to
avoid evil and in this manner is reducible to desire itself. (Anthony F. Beavers, 'Desire and Love in Descartes's Late Philosophy', History of Philosophy Quarterly, Vol. 6, No. 3 (Jul., 1989), pp. 279-294: 282-3.)
The emotions as a basis for collectivism
There is no reason why, given these primitive passions or emotions, collectivism should not be possible in some form. Co-operative inquiry, mutual responsibility, and citizen participation (Henry Tam, Communitarianism, London: Macmillan, 1998) could all be supported by the Cartesian passions. The exact mechanics by which collectivism could emerge from them is another matter.
The essential point is that once you have passions, you have the possibility not only of conflict and indifference but also of co-operation, which is the ground of collectivism. Appearances suggest that elements of co-operation, hence of collectivism, are real enough in contemporary life. In this sense 'collectivism actually exists'.