The switching glitches may be an issue with some high end bench meters at high resolution. The lower resolution meters usually have input protection with enough resistance to filter out the spikes and both ends. A good meter should also be somewhat tolerant to some spikes / variations in the signal. If the parallel connection causes problems there should be 2 meters at fault: one causing interference and one being a bit sensitive.
Some combinations of meters, even lower resolution ones, will have problems with charge injection from the automatic zero or chopper cycle. Usually I see this when measuring the input resistance of one meter using another, but it also shows up with high impedance sources.
I keep a couple of old multimeters which do not produce charge injection for sanity measurements. They use brute force with precision matched JFET input stages instead of automatic zero or chopping.
As for resistive part of input impedance, that is well defined in datasheets on all meters I have.
I would be really careful about that, especially with handheld automatic ranging meters. They often specify 1 or 10 megohm input resistance even when it varies significantly because of how the switching for the input divider is configured. They use a divider where different taps are grounded, which causes the input resistance to change. Moderate source resistances, or a high voltage probe, will then allow the reading to change on different ranges by an amount greater than the accuracy rating of the meter.
Most datasheets just say 1 or 10 megohms without specifying this. The alternative constant input resistance meters (1) sometimes specify 10 megohms with a tolerance like 1% or 0.1% which is much tighter than the variable input resistance case which is more like 10%.
This post shows what is going on with variable input resistance decade dividers on autoranging multimeters.
(1) Bench multimeters or manual ranging handheld multimeters, with some exceptions. I have yet to find a handheld automatic ranging multimeter which has constant input resistance, but I assume they exist. It is practically impossible to tell without measuring it.