Can Hard Cement Pointing Damage Old Bricks?

On older buildings, a hard cement mortar can sometimes contribute to damage. It is not guaranteed to cause problems, but it is worth understanding why it can.
Moisture has to go somewhere
Older walls manage moisture by letting it evaporate. When the joints are filled with a dense cement mortar, moisture is less able to escape through them, so it can be pushed out through the softer brick or stone faces instead.
What that can lead to
Over time, and especially with frost, this can contribute to spalling and erosion of the brick faces, where the surface flakes or crumbles away. Once a brick face is lost, it cannot be put back, only repaired or replaced.
It is not always a problem
Plenty of cement pointing sits happily on buildings for years. We would never recommend stripping sound pointing for its own sake. The question is whether it is actually causing damage on your particular wall.
When removal is worth considering
If you are seeing damp inside, or brick faces flaking next to noticeably hard joints, it may be worth assessing whether careful removal and a more compatible mortar would help.