Why is it “objections to moving”, not “objections to move”? [closed]
Because you need a noun to complete the phrasal verb objecting to XXX. That means you need a noun phrase there. Moving as a gerund is a noun. Move by itself is not one.
You seem to have been distracted into thinking that there is a to-infinitive involved here. There is not. That to is part of object to, not part of to move.