I think that most weight lifting favors isolation of the muscles, whereas Tai Chi favors integration of muscles. Using free weights, natural whole-body movement, or core exercises is probably less of a concern.
I think that truly high-level Tai Chi takes such a commitment that practicing things inconsistent with its approach is problematic for those on that path. Most of us, however, do not need such achievement to learn wonderful skills, strengthen our bodies, improve our health, and nurture the spirit. If this is your goal and you love weightlifting, I would do it. I do not believe Tai Chi is all or nothing.
If high-level Tai Chi is really your priority, then the conversation should really be about more than just whether or not to engage in weight lifting.