Can one really be a good Catholic if he is not a Thomist? If one is not an adherent of the teachings of St. Thomas Aquinas, can we say his Catholicity is suspect?
-Great question! Let me distinguish your question into a threefold division (in the old scholastic style).
1. Whether one can be a good theologian without adhering to (i.e., and reject) the teachings of St. Thomas?
a) Demostratio quia (proof of the fact, or "proof that"): Pope St. Pius X, who prescribed the main tenets of Thomism in The 24 Thomistic Theses, warned in Pascendi that "to deviate from St. Thomas, especially in metaphysical questions, is always attended by grave detriment."
b) Demonstratio propter quid (proof of the reasoned fact, or "proof why"):
Maj.: All doctrines to be held with assensu religioso ("religious assent") are held by all good theologians.
Min.: Many of Aquinas' teachings are doctrines to be held with assensu religioso.
Conc.: Many of Aquinas' teachings are held by all good theologians.
Probo Maj. ("I prove the major"): Per se patet ("it is self-evident"). Cf. Bl. Pius IX, Tuas libenter (1863), in Denzinger no. 1684:
Probo min. ("I prove the minor"): A great many of the teachings of St. Thomas, particularly his principles, have become, in the seven hundred years since his death, official church doctrines which, even if not de fide, are nevertheless taught authoritatively and, thus, are to be held with assensu religioso (e.g., some are sententiae communes, some are doctrinae tenendae, others are doctrinae catholicae, and a few even de fide---cf. the post on the Notae Theologicae).
For even if it were a matter concerning that subjection which is to be manifested by an act of divine faith, nevertheless, it would not have to be limited to those matters which have been defined by express decrees of the ecumenical Councils, or of the Roman Pontiffs and of this See, but would have to be extended also to those matters which are handed down as divinely revealed by the ordinary teaching power of the whole Church spread throughout the world, and therefore, by universal and common consent are held by Catholic theologians to belong to faith. But, since it is a matter of that subjection by which in conscience all those Catholics are bound who work in the speculative sciences, in order that they may bring new advantage to the Church by their writings, on that account, then, the men of that same convention should realize that it is not sufficient for learned Catholics to accept and revere the aforesaid dogmas of the Church, but that it is also necessary to subject themselves to the decisions pertaining to doctrine which are issued by the Pontifical Congregations, and also to those forms of doctrine which are held by the common and constant consent of Catholics as theological truths and conclusions, so certain that opinions opposed to these same forms of doctrine, although they cannot be called heretical, nevertheless deserve some theological censure.
2. Whether one can be a good Catholic without adhering to (i.e., being ignorant of) the teachings of St. Thomas?
a) Quia: The lives of many saints, especially the "simple saints," testify to this: e.g., St. Bernadette of Soubirous, St. Jean Vianney, The Little Flower, St. Thomas Kempis, etc.
b) Propter quid:
Maj.: Whatever is not necessary for salvation is not necessary for a life of sanctity.
Min.: Theology is not necessary for salvation.
Conc.: Ergo, theology is not necessary for a life of sanctity.
Probo Maj.: Per se patet. Cf. Prima lex salus animarum.
Probo Min.: Theology is a science. No science is required for salvation (rather, faith is). Ergo, etc.
3. Whether one can be a good Catholic without adhereing to (i.e., and reject) the teachings of St. Thomas?
a) Quia: cf. no. 1 above.
Maj.: All doctrines to be held with assensu religioso are held by a good learned Catholic.
Min.: Some of Aquinas' teachings are doctrines to be held with assensu religioso.
Conc.: Ergo, a good learned Catholic is one who adheres to the teachings of St. Thomas.
Probo: What was stated in no. 1 above applies not only to theologians but to all learned Catholics. Ergo, etc.
PS. In addition to Pope Leo XIII's Aeterni Patris (on the Restoration of Christian Philosophy), which you probably have already read, I wholeheartedly recommend Pope Pius IX's Studiorum Ducem (on St. Thomas).