Those accelerometers in the ADXL345 family respond to I2C commands when the SPI interface is de-selected. So if you are talking to other devices on the SPI bus, the accelerometer can misinterpret that as I2C.
There is no way to turn off the I2C in the chip. You have to use multiple SPI buses or a buffer chip that can disconnect the ADXL when it is not selected.
What adapter do you have for the SD card? The SD specification uses 3.3V but the Nano is 5V. Some cards will work at 5V for a short time before failing.
The ADXL is also 3.3V.