I have my own business, and set up a Roth 401K, max $15,500 contribution, and a profit sharing plan, maximum 19K for a total contribution of about $44000.

I just started a State government consulting job, with a 457 plan-- they say my max this year is $15500, and that the 401 K of my business doesn't effect the maximum for the 457 plan. Is the reverse true? In other words, does the $15500 contribution to a 457 plan affect my maximum contributions to my 401K plans with my own business?

The salary deferral to the 457(b) plan does not affect the salary deferral to the 401(k) plan and Vice versa.
Therefore, if you are eligible to contribute to both plans, you can defer up to $15,500 to your 401(k) plan, plus an additional $15,500 to the 457(b) plan

And, if you are over 50, then catch-up deferral contributions can be done to both also.

Sometimes the word "consulting" implies an independent contractor relationship rather than an employee relationship. Are you an employee?

If you are an independent contractor, it is still possible that a gov 457(b) plan allows you to be eligible for the plan.

Thanks for your information. Is this still valid nowadays? Thanks.

Yes. The 2 limits do not offset each other, and yes, an independent contractor can participate if the document has language to allow that.