What I have:
GSM 900 repeater
900 - 2400 MHz MIMO antenna 2xSMA
MIMO 4G Router works with 1800 MHz LTE
Is it a good idea to connect GSM repeater via SMA splitter to one of the antenna cables? Will the devices interfere with each other?
There are different ways to “split” a coaxial connection, and some of them are wrong.
The simplest, cheapest thing you would find in SMA form factor is a tee, a small device with 3 SMA (or other coaxial) connectors. You should not use this because it will allow the transmission of one device into the receiver of the other, possibly damaging it with the high power. Also a tee used without care creates an impedance mismatch. Correct uses of a tee are either carefully-measured cases like matching stubs, connecting high-input-impedance test gear such as an oscilloscope, or very low-frequency applications where transmission line length is unimportant.
You could use a power divider (or combiner, it's the same thing) — this is the same type of device as used to connect multiple TVs to one cable-TV or antenna cable. This will work in principle but the devices may interfere with each other, and the incoming signal will be reduced by 3 dB.
The best solution in this case, where the two devices are widely separated in frequency, is known as a diplexer or duplexer. It has three ports, one which you would connect to the antenna and two more which are frequency-specific. You would choose a diplexer whose lower-frequency range includes 900 MHz and whose higher-frequency range includes 1800 MHz.
Because the diplexer contains filters, it will reduce interference between the two devices (if any). In fact, it might be even better than using separate antennas — but it depends a lot on the characteristics and quality of the devices' receivers and transmitters whether there will be a problem at all in either case.