Spiritual:
(1Cor 2:13-16) These things we also speak, not in words which man's wisdom teaches but which the Holy Spirit teaches, comparing spiritual things with spiritual. But the natural man does not receive the things of the Spirit of God, for they are foolishness to him; nor can he know [them,] because they are spiritually discerned. But he who is spiritual judges all things, yet he himself is [rightly] judged by no one. For "who has known the mind of the LORD that he may instruct Him?" But we have the mind of Christ.
Religious:
(Jas 1:26-27) If anyone among you thinks he is religious, and does not bridle his tongue but deceives his own heart, this one's religion [is] useless. Pure and undefiled religion before God and the Father is this: to visit orphans and widows in their trouble, [and] to keep oneself unspotted from the world.
Being Spiritual is having the mind of Christ. How can someone have the mind of Christ and yet not visit orphans and widows in their trouble and not being holy?
Hence, based on Scripture, you can't be spiritual and not religious. Being religious is a subset of being spiritual.