If i start off with a theme team like say Justice society and i make a team of

FL003 Jesse Quick
151 WOL106 Jade
145 AN049 Green Lantern
D10A011 Green Lantern
479

then would using the power BATTLEFIELD PROMOTION: PASS THE TORCH from D10A011 Green Lantern ruin the theme team since the Green Lantern that comes in does NOT have the Justice society keyword?

or would i still get my theme team probs since i did start the game with a theme?

Theme teams are made during force construction so if you promote mid game you still are a theme team.
Short answer is yes

You will still have a theme team, but I'm 99% sure that the replacement character would be unable to use theme prob because no JSA keyword.

This is correct.