We highly recommend this record be listened to loud.
We'd recommend you to book your flight early.
Why do we use a bare infinitive for the first and not for the second
Notice that it is grammatical (and perhaps more idiomatic) to say "We'd recommend you book your flight early."
Thus, you have an option to use a bare infinitive in both cases. There is no general rule saying that passive infinitives must be bare although in this specific case I agree that you cannot idiomatically just plunk a "to" in front of the passive infinitive without other changes to the sentence.
We highly recommend this record be listened to loud.
"Be" here is a subjunctive, not a bare infinitive, although the two are identical in form.
This is elliptical for "we highly recommend that this record be listened to loud".
We'd recommend you to book your flight early.
This is ungrammatical. "Advise" would work here, because "advise" can be followed by the person being advised (as the direct object) followed by a "to" clause. "Recommend" can't. The direct object for "recommend" is the recommendation, not the person being advised.
("We'd recommend your flight to be booked early" would be grammatical, although very awkward. The whole phrase "your flight to be booked early" then effectively functions as the direct object. There is no implied "that" after "recommend" here.)
"We'd recommend you book your flight early" would work. (It is elliptical for "We'd recommend that you book your flight early.)
recommend, advise, suggest and several other verbs do not take "to infinitives".
We recommend this book to you.
We recommend you read this book.
We suggest you read this book.
We advise you go now.
We advise you to go. [not a to infinitive as the to does not come after the verb advise]
[We advise to go now. BUZZER]
"Recommend to" is not grammatical in English. Except in sentences like: The book was recommended to me. Passive sentences.
We recommend you book your flight early.
We highly recommend you listen to this record at a high volume.
We highly recommend this record be listened to at a high volume.
"be listened to" is a passive construction from "To listen to a record".
"The record was listened to last night. I can see the scratches on it."