How should I get rid of a xylene and naptha mixture I have?
It's about 3/4-1 gallon.
Can I take it to hazardous waste in a plastic jug? Will this arouse suspicions?

Distillation is not an option. My extraction days are over. It will only be natural methods from now on.

You can use it as fuel. Not for your car obviously but the same things people use lighter or starter fluid for the bbq for.

Unless you have a good reason for taking it to chemical waste disposal I'd be careful about that. In the end they will probably throw it in an incinerator for energy. Lots of hydrocarbon chemical waste goes to that purpose.

This is exactly what SWIM's doing. He's keeping said solvents in a bottle labelled for said uses ("Camping fuel", and he mostly uses it when camping.