I practice both Yoga and Tai Chi and have done for 12 years. I find they go together perfectly. I recommend that Yoga practitioners try an internal martial art, and vice versa.
To begin with, it might be better to practice one first and then the other, depending on your background.
On starting Yoga, I had already trained in a few martial arts from a young age, so as a ‘body’ person I could pick things up relatively quickly and differentiate without getting confused.
When you practice Yoga, be doing just that. Same gos with Tai Chi. If you’re a complete beginner to both, dedicate some time to just one. This is the safest way to do things, and avoids confusion. There are many different approaches in both arts as it is, without making things more difficult.
As a point of interest, Tai Chi Chuan evolved out of the Shaolin Arts which in turn were influenced by Yogic techniques.