Home heater and a/c coming on at the same time all electric system

Brand name, model number

You probably need a new heat sequencer

Try to separate the cause... diconnect the t-stat wires first.. if it continues the problem is in the unit itself i.e. sequescer, circuit board,. if not,. it's going to be in the stat.. stuck ,shorted.. and yes.. model number would help lol... good luck

Didn`t understand,, did you replace the sequenser?
If not I would, it's the cheapest part you can start with