According to A Student's Introduction to English Grammar (pp. 70, 297, 303), the object is a kind of complement which almost always has the form of a noun phrase (NP). Any object is a complement, but not any complement is an object.
Everyone likes her.
Her is a complement, and since it's an NP — consisting of a single pronoun, her — it is also an object.
The clauses in your examples are content clauses, not noun phrases. Therefore, they aren't objects. A Student's Introduction seems to simply call them complements or, more specifically, content clause complements (a complement that has the form of a content clause). It doesn't matter whether you leave the that in or out; the grammar doesn't change.
The Cambridge Grammar of the English Language also uses these terms (p. 246).
Subordinate clauses show varying degrees of similarity to NP objects, but (with minor exceptions) we prefer to use the more general term complement for them in view of the absence of well-motivated criteria to determine which are objects and which are not.
It also provides evidence as to why a content clause cannot be an object. Here are just three of the points it makes (pp. 1018–1019). I've rewritten them to be a little bit shorter and easier to read.
(a) Objects almost always come immediately after the verb
Aside from a few special cases, the object always comes immediately after the verb. This restriction doesn't apply to content clauses.
*He opened slowly the door.
He denied categorically that he had spoken to her.
*He returned to me the key.
He mentioned to me that he was leaving.
(b) There are verbs which cannot take an NP object
I often [marvel that intelligent people can at times be so petty].
She will [vouch that I didn’t leave the house until six o’clock].
You cannot say, for example, *Everyone marveled his courage.
(c) Declarative content clauses cannot occur as complements of prepositions
He rejoiced [at her decisive victory].
*He rejoiced [at that she had won so decisively].
To use a content clause in the second example, we'd have to omit the preposition at: He rejoiced that she had won so decisively.
Wikipedia editors seem to follow a different analysis, probably the traditional ("old") one:
While the typical object is a pronoun, noun, or noun phrase, objects can also appear as other syntactic categories.
Follow the link and take a look at the table there, if you're interested.
An asterisk (*) before an example sentence indicates that it is ungrammatical.