Trae Cooper (paraphrased)
Why are Invested objects like metalminds and Hemalurgic spikes able to be Pushed and Pulled on, but Shardblades and Shardplate, which are also invested, are not susceptible to Pushing and Pulling?
Brandon Sanderson (paraphrased)
There were a few concepts that he outlined in answering this question.
1.) The ability to Push/Pull an Invested object is predicated to the amount/power of the Investiture.
2.) Further, Invested objects also gain resistance to pulling/pushing based on proximity to soul possibly via the soul. An example given is that a Hemalurgic spike touches the blood of the person, and from there is now part of both the Spiritual Realm and the Physical Realm. This provides what Brandon termed a kind of "soul interference," based on its proximity to the soul.
This further explains why Vin required more than normal power to Push/Pull the metalminds from the Lord Ruler, because of their proximity to his soul, via the Spiritual Realm.
3.) The amount of Investiture is relatively low on Scadrial, whereas worlds like Sel and Roshar are pushing around "high power" according to Brandon. I interpreted this to mean that Hemalurgic spikes and metalminds have low amounts of Investiture compared to Shardplate and Shardblades.
Brandon said that theoretically you can Push/Pull Shardblades and Shardplates but you would need to wield an incredible amount of power. One example he gave that could so such as a thing is that if you were a Mistborn wielding the full power of the Well of Ascension, you could Push/Pull Shardblades/Plate.