I'm okay with the current version, though I have few minor comments below.

quoted

Introduce helper functions to access the 'SSCR0' and 'SSCR1'.

Like you said in the summary there are many accessors to many registers, not
only cr1/cr0. Perhaps, you may extend your commit message.

OK.

In any case
Reviewed-by: Andy Shevchenko <andriy.shevchenko@linux.intel.com>

OK.

quoted

+
 /*
  * Read and write LPSS SSP private registers. Caller must first check that
  * is_lpss_ssp() returns true before these can be called.

@@ -234,7 +301,7 @@ static int null_writer(struct driver_data *drv_data)
 	void __iomem *reg = drv_data->ioaddr;
 	u8 n_bytes = drv_data->n_bytes;

-	if (((read_SSSR(reg) & SSSR_TFL_MASK) == SSSR_TFL_MASK)
+	if (pxa2xx_spi_txfifo_full(drv_data)
 		|| (drv_data->tx == drv_data->tx_end))

Just wondering if those two could fit one line.

No, if make the two in one line, it is 84 characters.