They aren't very specific about it, but LVDS transmitters do have some modest CM impedance, and a default CM voltage. They are usually diagrammed as a CCS-fed H-bridge, but the detail that they're all-NMOS I think is actually salient: the high side MOS are not switches, but source followers, and their gate voltage can be tuned to set CM output voltage. The effective circuit is, a source follower (whichever line pulled mostly-high), the transmission line in series, then the CCS pull-down. Source follower impedance can be quite modest (100s ohms) hence the CM voltage is allowed to mostly float, but is gently pulled to level this way. CM impedance also provides some damping, ensuring that CM voltages don't run away due to CM-DM mode conversion (imbalance, routing error, etc.) at unlucky (resonant) frequencies.
A split termination is useful when a better-defined CM impedance is required. This can assist filtering on external connections (cables, etc.), obtain a ground reference where none was present otherwise (e.g. ground-less isolated RS-485), but can also create problems where there was none before (for the same example, the terminator and RS-485 driver will have slightly different ideas of V_CM, and therefore some CM emission is inevitable as the driver keys on and off).
Differential is indeed filtered by such an arrangement, but in a very specific way. Note that the line itself forms a filter network with the termination resistor(s). We have the special case that the line is an all-pass filter when terminated into R = Zo, giving good signal quality and a nominal time delay.
Note that we cannot terminate in the middle of a line, where insertion loss and reflection result instead. Termination is only applicable to point-to-point links, and terminal (end) nodes on multi-master (like RS-485) buses. This greatly limits the filtering options for mid-bus nodes, and is why they generally require a ground connection along with the signal pair.
Tim