What that statement seems to mean is that you believe in God but do not follow any organized religion. You have faith but it is strictly personal.
The implication is that faith is good but official religion is corrupt.
The language is sloppy because religion, the acts of religion, are much broader than simply belonging to a body of believers.
"Religion consists in an operation by which man honors God by submitting to Him; and this operation ought to be in harmony with Him who is honored, and with the one offering homage." Aquinas
There are therefore three major types of religious acts.
1. Raising the heart and mind to God: acts of the theological virtues of faith, hope and love.
2. Bodily actions ordered toward God: acts of worship like vocal prayers, sacrifices offered to God, prostrations, kneelings, bowings, signs of the cross, arms outstretched, etc.
3. Acts of love toward our neighbor, for love of God.
What is involved here is an error of logic. People claim to reject religion because of the sins of religious people. But they are all the while doing acts of religion while discriminating those they consider "religious." You don't hate breathing air because people that breath air happen to sin! Sinning and breathing air are two different activities. Religion is not a sin even though all religious people happen to sin (except Jesus and Mary). Identify and reject the sin, and try to save the sinner, among whom you are also one in need of saving.
P.S. "Spiritual" people are sinners too! I recall an interview with one of John Lennon's lovers who was initially so much infatuated with the music idol until she realized how morally dissolute that man was. She was shocked that someone so "spiritual" could be so bad! Welcome to the real world. It's not religion that makes people bad. Sin does that, sin alone!
God did not make evil, devils and men did (beginning with Adam and Eve with the ancient serpent against God!).
De Trinitate Commentary Q. 3, Art. 2, Resp. How Faith is Related to Religion (Excerpt)
Now since He who is reverenced is a spirit, He cannot be approached by the body, but only by the mind; and so worship of Him consists chiefly in acts of the mind by which the mind itself is ordained to God. These acts are principally those of the theological virtues; and in accordance with this, Augustine says that God is worshiped by faith, hope, and charity, to which are added also the acts of the gifts ordained toward God, such as those of wisdom and of fear.
But because we who honor God are also possessed of bodies and receive our knowledge through bodily senses, there is the necessity that certain physical actions accompany the worship of God, not only that we may render service to God with our whole being, but also that by these bodily actions we may arouse in ourselves and in others acts of the mind ordained to God. Wherefore Augustine says in his book, De cura pro mortuis habenda: “Those who pray make the members of their bodies conform to their acts of supplication when they genuflect, extend their hands, or prostrate themselves upon the ground, or perform any other visible action; and although it is their invisible will and the intention of the heart that is known to God, it is not unseemly that the human soul should so express itself, but rather by so doing man stirs himself to pray and to lament his sins the more humbly and fervently.”
Hence, all acts by which man subjects himself to God, whether they are acts of mind or of body, pertain to religion. But because those things that are rendered to the neighbor on account of God are rendered to God Himself, it is evident that they also pertain to this same subjection in which religious worship consists; and so to one diligently considering the matter it is apparent that every good act pertains to religion. Hence Augustine says (loc. cit.): “True sacrifice is every work done that we may adhere to God in holy companionship; however, in a certain order.” First and foremost, those acts of the mind ordained to God pertain to the worship which we are speaking of. Secondly, there are acts of the body intended to arouse reverence of mind or to give expression to it, such as prostrations, sacrifices, and the like. Thirdly, there also pertain to divine worship all other acts ordained to the neighbor for the sake of God.