The chances of damaging clay tile by walking on it depend on the tile quality, age, and installation. Any time you walk on clay tile you are taking a chance on breaking some. You should make an effort to step on headlaps only. Shift your weight slowly. With certain tile profiles your foot can span two tiles, reducing the amount of weight on each one. Old tile will be chipped, broken, loose, or have biological growth visible. Don’t walk on old tile.
Biological growth (like the lichens visible here) and broken or displaced tile are signs of old, fragile tile likely to break if walked on.