How do i get rid of a power-spike from consumer electronics?
Two possible causes, with a bonus one:

1- Speaker does evil things to mains voltage

2- Speaker sends common mode noise into signal cables, which zaps the TV.

3- Speaker radiates enough EMI through the air to reboot the TV (unlikely)

To distinguish, unplug the audio cables from the speaker, it shouldd now be only connected to the mains. Feed it some music from an ungrounded device like an iPod/phone/whatever, or just put a cable in the RCA and stick your finger on the center pin at the other end, that will create enough BUZZZZZ to make the speaker think there is signal and it should turn on.

If the TV does not reboot, then cause 2 should be suspected.

If the TV reboots while the speaker is connected only to the mains (no other cables) then this rules out cause 2.

Now use an extension cord to connect the speaker to the mains, but still in the same socket. Repeat. Most likely the TV still reboots.

Move the speaker away (that's why you put an extension cord), repeat.

TV still reboots, that rules out cause 3 "airborne EMI" which was unlikely anyway.

Connect the extension cord to another outlet away in the house. Repeat.

If TV does not reboot, then the speaker does have an inrush current or other mains borne EMI problem, or the outlet your TV is plugged in has high resistance, oxidized old wires and the like.

To be continued after you perform the tests...