Running synths into a guitar amp is something you should do with caution.
Understand your synth output, audio interface and most tape inputs are designed for what's called a "line level" signal.
This is a lot louder than a typical guitar output which is at "instrument level". This is what your amp is designed for -not a synth. When running a synth into your guitar amp you're literally pumping more electricity into your amp than it was designed for.
You can really get some great tones from your synth doing this but a low end synth frequency through an amp designed specifically for guitar frequencies can do exactly as you describe --and you could easily mess your amp up. An EQ can only do so much, they're not the same as a high pass filter / limiter.
When running a synth into a guitar amp (something I do often) definitely begin with the amp and synth gains at the lowest setting and creep them up, slowly. Absolutely avoid running any frequencies / volumes into any amp that cause crackling noise. Even certain "crackling" at 0 db should be avoided, if possible. I suspect most noise / PE stuff with intentional "crackling" is often mastered at lower levels (or even performed on throwaway gear/broken amps etc) and even then those tracks should probably be played back on larger systems with caution, as well.
Also, using a decent mic and stand to record means you shouldn't need to crank the amp that high. If you need to use a HPF / limiter between the synth and amp that could also help, but always keep the levels and frequencies out of the "danger zone" if you want your amp to live. Those jc 80s weren't exactly cheap.
