The comparison to hatzalah isn’t exactly equitable because no one says a mi sheberach for hatzalah. If it had become accepted in many communities to say a mi sheberach for hatzalah and others communities did not, yet hatzalah was equally helping everyone, I could see how it might be perceived as a lack of hakaras hatov for those communities who don’t say it.
The fact that non religious Jews don’t value the protective value of Talmud Torah and don’t show hakaras hatov for it does not absolve us of our hakaras hatov towards them for protecting us as well.
The hakaras hatov we show to soldiers is not simply for protecting us. If that were the case, then Bnei HaTorah should be receiving at least equal hakaras hatov. The hakaras hatov for soldiers is also for the sacrifice and risk they put themselves in to protect us. They literally put their lives on the line to stand between us and our enemies. Bnei HaTorah do not risk nearly as much and that should be taken into account when we try and compare who “deserves” more hakaras hatov for protecting us.