You have to note the tense of the head clause as well as that of the subordinate clause.
The main clause in each of your first two examples has its verb in present form, indicating present tense: It is known. What is known now is a fact about the past.
The Form 1 version expresses that past fact with a that clause, which employs a finite (tensed) verb, was. Here it is cast in the past form to express its past reference.
The Form 2 version expresses that past fact with an infinitival clause, which employs a non-finite verb, the infinitive.
An infinitive verb has no tense; the clause has to 'borrow' its tense from the main clause. But if you write simply to be—John Lennon is known to be interested in oriental religions—the result is an absurdity: this claims that John Lennon, who has been dead for more than thirty years, is interested right now in oriental religions.
To indicate the pastness of Lennon's interest, we replace the simple infinitive with a perfect infinitive: to have been.
Now look at your second pair of examples. The verb in the main clause, was said, is cast in the past form, indicating that the 'saying' took place in the past.
The finite verb in the Form 1 that clause is also cast in the past form, was, indicating that the opposition to change took place at the same time as the saying.
In this case, the verb in the Form 2 version is cast as a simple infinitive, to be; this properly borrows its tense reference from the main clause.
If instead you wrote He was said to have been against ..., you would be indicating that it was said, at some time in the past, that he had been opposed to change at some prior time, before the saying.
Note that with a that clause you can also express a time reference subsequent to the time of the main clause:
Form 1a. It is said (now) that he will run for President in the next election (in 2016).
Form 1b. It was said in 2010 that he would run for President in the next election (in 2012).
You can even mix your forms to express a "double future":
Form 1c. It was already being said in 2012 that he will run for President in the next election (in 2016).
You cannot do this with the infinitival clause, because will has no infinitive form. To express this with an infinitival you have to use a different verb, such as intend:
2a. He is said (now) to intend running for President in the next election (in 2016).
2b. He was said (in 2010) to intend running for President in the next election (in 2012).
And the infinitival cannot handle the double future—you have to make the after-now reference explicit:
2c. He was said (in 2010) to intend running for President in the 2016 election.