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No, grapple and shoving attacks can be performed on creatures only.

You quoted the relevant rules: both attacks require that the target be a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is neither a creature, nor an object. It does not provide any stats block, nor point to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that might suggest a DM ruling in that sense.
• Spiritual Weapon is...a weapon. You can check the difference with a Flying Sword, which is technically a creature and hence can be grappled and/or shoved.
• Unseen Servant is not a creature either.

No, grapple and shoving attacks can be performed on creatures only.

You quoted the relevant rules: both attacks require that the target be a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is neither a creature, nor an object. It does not provide any stats block, nor point to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that might suggest a DM ruling in that sense.
• Spiritual Weapon is...a weapon. You can check the difference with a Flying Sword, which is technically a creature and hence can be grappled and/or shoved.
• Unseen Servant is not a creature either.

A DM has always the final word.

The above considerations are based on the direct application of the rules. A DM has the final decision, they may allow these kinds of attack even for objects and for other entities (such as an Unseen servant).

No, you can perform grapple and shoving attacks only on creatures.

You quoted the relevant rules: both attacks require that the target is a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is not a creature, nor an object. It does not provide any stats block nor points to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that may suggest a DM ruling in that sense.
• Spiritual Weapon is... a weapon that is technically a creature and hence you can grapple and/or shove it. You may check the difference with a Flying Sword.
• Unseen Servant is not a creature either.

No, grapple and shoving attacks can be performed on creatures only.

You quoted the relevant rules: both attacks require that the target be a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is neither a creature, nor an object. It does not provide any stats block, nor point to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that might suggest a DM ruling in that sense.
• Spiritual Weapon is...a weapon. You can check the difference with a Flying Sword, which is technically a creature and hence can be grappled and/or shoved.
• Unseen Servant is not a creature either.

No, grapple and shoving attacks can be performed on creatures only.

You quoted the relevant rules: both attacks require that the target be a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is neither a creature, nor an object. It does not provide any stats block, nor point to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that might suggest a DM ruling in that sense.
• Spiritual Weapon is...a weapon. You can check the difference with a Flying Sword, which is technically a creature and hence can be grappled and/or shoved.
• Unseen Servant is not a creature either.

No, you can perform grapple and shoving attacks only on creatures.

You quoted the relevant rules: both attacks require that the target is a creature.

In particular, about your listed entities:

• Bigby's hand is an object, not a creature: it can grapple because its description says so, under the Specific beats general principle.
• Guardian of Faith is not a creature, nor an object. It does not provide any stats block nor points to a Monster stats block. Moreover, the spell description does not provide any partial stats (AC, HP, attacks) that may suggest a DM ruling in that sense.
• Spiritual Weapon is... a weapon that is technically a creature and hence you can grapple and/or shove it. You may check the difference with a Flying Sword.
• Unseen Servant is not a creature either.