Yes, after witnessing these incidents (when watching matches of in-game friends), every time when a red card is shown to opponent and I would always change my team to ‘suit’ the situation better. Personally I never lost any match after opposition got a RC with this or previous account having played 500+ matches.
The way I look at it is in 2 ways:
1) 1 of my players, in that match, is a RC-inducing factor (plus FK- inducing), so he could ‘only’ perform best when he is being marked by an opposition player but not afforded empty space - and he may even be counter-productive when unmarked after opposition player gets a RC, and so the best solution is to switch him to be marked by the worst-rated opposition player and wait for more FKs, with the vacated space taken by another of best-rated players of mine
2) That opposition player got sent off was the one who always played the mis-placed pass (midfielder/defender) or miss certain goals (ST/AM) - the latter personnel should always be noted. Inevitably, engine calculation for opponent will turn more positive even when with a man down in these specific circumstances, so my solution is to tune to a more defensive formation and order instead. Basically both defence and midfield is +1 player against opponent to minimise chances conceded and win by counter goals.
The ‘worst possible’ thing to do is doing nothing after opposition red card. Engine calculation WILL have changed and so should our team adapt accordingly.