If an MRI reveals an oblique tear through disc proper of triangular fibrocartilage, will playing tennis/ golf do further damage?

Yes over time. If you are under 40 the tear is probably from repetitive trauma and will get worse over time with activities that cause ulnar deviation (towards the little finger). If older the tear is probably degenerative and may or may not get worse with use.
Probably not. I see routinely patients with linear tears in the central TFCC, and there is no good correlation between pain symptoms and these tears. As long as your wrist is not in pain, playing golf should not by itself make things worse. A good golf glove may also help to protect your wrist.
Do whatc comfottable. These can be medlesome chronic problems usually caused by a fall on outstretched hamd foosh injiury avoid pushups or weight bearing through wrists use pain as your guide good luck.