This all really depends on what you mean by Realism. In terms of realism meaning that things exist independent of mind, then CT is realist yes. Its not “things” though, by which I mean substances such as tables or chairs or chemicals which exist independently of mind. Its the sabhāva-dhammas, which are simply ephemeral qualities (hard, soft etc) and barely exist. If, further, by realism in terms of perception you mean Direct Realism then CT doesn’t agree, since with Direct Realism when you see a tree you are really seeing a tree as it is, which exists independently of mind. For CT this isn’t the case, because the “tree” is a concept which doesn’t really exist. What the person sees is a concept, and most people only operate in a conceptual and so ultimately false world. Instead what happens is as I described earlier. If we take the eye base a colour impinges upon the eye and a visual sense door consciousness arises. Immediately following this, after 17 mind moments, the colour ceases to exist. Within that time you get the, as I said, an eye-consciousness. This immediately passes away and a receiving consciousness arises which has a mental reflection of the image. Following that there are the cittas of investigating > determining > Javana > and finally two cittas of registration. Its only at the later stage that one recognises “red” and not before at the 5 sense consciousness stage, with this recognition occurring in the mind base. So, according to CT, you are only ever aware of a reflected image of the sabhāva-dhamma of red. CT then does not support the idea of Direct Realism.
I’m also not a follower of Mahāyāna, so please don’t persist in calling me one.