This is what the datasheet has to say about it:
4.3 Output Capacitor
The MCP1825/MCP1825S requires a minimum output
capacitance of 1 μF for output voltage stability.
Ceramic capacitors are recommended because of their
size, cost and environmental robustness qualities.
Aluminum-electrolytic and tantalum capacitors can be
used on the LDO output as well. The Equivalent Series
Resistance (ESR) of the electrolytic output capacitor
must be no greater than 1ohm. The output capacitor
should be located as close to the LDO output as is
And the input capacitor (4.7uF):
4.4 Input Capacitor
Low input source impedance is necessary for the LDO
output to operate properly. When operating from
batteries, or in applications with long lead length
(> 10 inches) between the input source and the LDO,
some input capacitance is recommended. A minimum
of 1.0 μF to 4.7 μF is recommended for most
applications. For applications that have output step load
requirements, the input capacitance of the LDO is very
important. The input capacitance provides the LDO
with a good local low-impedance source to pull the
transient currents from in order to respond quickly to
the output load step. For good step response
performance, the input capacitor should be of
equivalent (or higher) value than the output capacitor.
The capacitor should be placed as close to the input of
the LDO as is practical. Larger input capacitors will also
help reduce any high-frequency noise on the input and
output of the LDO and reduce the effects of any
inductance that exists between the input source
voltage and the input capacitance of the LDO.
So actually there is no specification that the input capacitor should be ceramic either, I would suggest then that electrolytic capacitors will be absolutely fine for this application.
By the way, LDO just stands for Low Dropout. To quote Wiki -
A low-dropout or LDO regulator is a DC linear voltage regulator which can regulate the output voltage even when the supply voltage is very close to the output voltage.