In the FIFA Laws of the Game, there is no such thing as a "soft" or "hard" red card. Many observers will use these terms to describe a clear offense (hard) versus a questionable offense (soft) in order to communicate their disagreement with the referee's decision.
In NFHS (U.S. High School) rules there is no mention of "soft red" exactly. For certain offenses, the punishment is a disqualification (send off) of a player but where a team-mate may replace the player. This is signaled by showing a red and yellow card simultaneously. Players, coaches, spectators, and referees all colloquially call this a "soft" red.
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In soccer, a "soft" red card is a term used to describe a red card that was received for an offense that the speaker did not believe merited it.
It has another, very specific meaning in U.S. High School soccer. In the modified rule set of high school soccer a red/yellow combination may be shown to a player to indicate that the player is being disqualified but may be replaced.
I take it you mean where the commentator has said "for me, that's a soft red card". This basically means the referee has been especially harsh on the player, maybe the challenge or offence only warranted a yellow.
A red card in football terms is an immediate sending of, a yellow is for a less viscous challenge and that if you get two of these you get a red.