How are the passband filters in SDRs able to select such a wide range of frequencies?
I think many SDRs either have no filter or have a very wide filter at RF. Really, the main filtering required is at IF. And that can be a wide, fixed filter, followed up by narrower filters implemented with DSP. There is usually also some band switching to enable receiving inputs near our on the wrong side of the IF.

Consider the USRP-2954 SDR (block diagram from http://zone.ni.com/reference/en-XX/help/373380G-01/usrphelp/2954_block_diagram/):



The frequency range is 10 MHz to 6 GHz.  For 500 MHz to 6 GHz, a single conversion is used to translate to baseband.  No tunable filters are required here, only fixed 80 MHz low pass filters between the mixer and the ADC.  A fixed 500 MHz or so high pass filter to remove anything in the vicinity of the baseband might be a good idea to avoid aliasing, not sure why it's not there.  For 10 MHz to 500 MHz, two conversions are used: one to convert up to 2.44 GHz, then one to bring that back down to baseband.  Again, this requires only a few fixed filters.  

The HackRF One is similar (block diagram from http://www.dolstra.nl/Ham-radio/SDR_Tranceivers/HackRF%20One%20SDR/HackRF%20One%20SDR.htm):



In this case, there are two image reject filters (one fixed high pass, one fixed low pass).  Signals can be routed through one of those filters and a frequency converter or bypass the front end frequency conversion entirely.  None of this requires tunable filters.  The IF in this case is 2.3-2.7 GHz, converted to/from baseband with a MAX2837.  

Also, if you really need an adjustable RF bandpass filter, they do exist, they just aren't cheap.  And they have been around for quite a few years.  YIG tuned filters can have a decently narrow bandwidth and can be tuned over several GHz.  They are relatively common in RF test equipment that works at relatively high frequencies (10 GHz+)