SPI (3 wire) implementation using PIC
The SPI protocol uses separate input and output signals, which are always active (although input or output bits are often ignored).

The DS1302 uses a single I/O pins which is either input or output, depending on the type of the transaction, and where in the transaction you are. (There is no standard for this protocol.)

Plain SPI does not work. However, you can connect both SDI/SDO pins to the I/O pin as long as you ensure that only one of them is active. In other words, ensure that the SDO pin is disabled (configured as GPIO input) whenever the DS1302 is outputting something.
However, your MCU does not allow to reconfigure a single pin (SSPEN enables all three SPI pins), so you cannot use the SPI module and have to do bit-banging instead.