Turntable Causes Speaker Cones To Excessively Move Rapidly

All "rumble" or "subsonic" filters are not alike.  AND, both your subwoofer and speakers are vented...which makes them susceptible to noise generated by normal record playback at frequencies below their "cutoff point"...tuned resonance frequency,  For the REL this is probably around 20Hz, and for the Sopra 1s around 50Hz...so both are wide open to oscilate when fed  0-12Hz.  The Lux filter is probably 6dB/oct below 20Hz.  You need a steeper filter.  This can be obtained with an outboard phono preamp whose design inludes a sharp filter.  The other solution is to use sealed box speakers and subwoofers that are "loaded" to roll off below their resonance frequency.  

@otimmons I am using a Ortofon 2M black lvb and it still does it. Not sure if that would be close enough to yours. 

The Ortofon has a compliance of 22 compared with 22.5 for the Shure. The resonant frequency in a 22g tonearm is 6 Hz. Anything less than 8 can give the unwanted resonance. you may have a mismatch.

look for a cartridge with a dynamic compliance less than 16, preferably less than 13 x 10^-6 cm/dyne

buy a KAB Rumble filter and call it a day.  It took away the oscillating with my former VPI Prime.  I no longer have the problem with my Technics SL1200G and no longer use the filter.

lewm had asked you in another thread what headshell you are using.  I don't remember your answer.  @otimmons is giving you that same information in a different format as have others.  It does sound like you have a resonance problem.  This is caused by the mass of the arm and headshell being too high for the compliance of your cartridge.  If the resonance of the cartridge/arm assembly falls outside the range of 8-12 Hz there is a problem.  In your case it is likely the resonance is under 8 Hz and that is why your speakers are pumping.  This problem is more common than most people realize.  Step 1.  Use the OEM headshell, which is < 8 grams including azimuth adjustment and is the lightest weight one available.  That might be enough.  If not, Step 2.  Chose a cartridge with less compliance.  Staying with a MM, I have had excellent results with the new Audio Technica VMN60xSL for example on my SL1200GAE.  It works better than my 2M Black LVB on that turntable in part because of the compliance difference.  With other arms, the more expensive Ortofon more than holds up in the comparison.  Arm compatibility is just as critical as picking the best cartridge.