Catholicism - Consequences of not believing in all dogmas What are the consequences according to the Catholic Church for members of the Catholic Church in case of not believing in all dogmas?

For example 


Rejecting the notion of the bodily ascension or assumption into heaven (alive) as introduced in 1950
Not believing in Transubstantiation during Eucharist but understanding it as a symbolic act like the Lutherans do


All other teachings and dogmas would be believed.
This is an interesting question. Many people are not particularly clear on what dogmas really are and why they are important. The Catechism of the Catholic Church says:

The dogmas of the faith
88 The Church's Magisterium exercises the authority it holds from Christ to the fullest extent when it defines dogmas, that is, when it proposes, in a form obliging the Christian people to an irrevocable adherence of faith, truths contained in divine Revelation or also when it proposes, in a definitive way, truths having a necessary connection with these.

Therefore, dogmas are those propositions which Christians are obliged (that is, they must) to believe irrevocably. They are truths which, if not believed, bring down the whole edifice of the Faith and make it empty.
The Code of Canon Law further states:

Can. 749 §1. By virtue of his office, the Supreme Pontiff possesses infallibility in teaching when as the supreme pastor and teacher of all the Christian faithful, who strengthens his brothers and sisters in the faith, he proclaims by definitive act that a doctrine of faith or morals is to be held.
§2. The college of bishops also possesses infallibility in teaching when the bishops gathered together in an ecumenical council exercise the magisterium as teachers and judges of faith and morals who declare for the universal Church that a doctrine of faith or morals is to be held definitively; or when dispersed throughout the world but preserving the bond of communion among themselves and with the successor of Peter and teaching authentically together with the Roman Pontiff matters of faith or morals, they agree that a particular proposition is to be held definitively.
§3. No doctrine is understood as defined infallibly unless this is manifestly evident.
Can. 750 §1. A person must believe with divine and Catholic faith all those things contained in the word of God, written or handed on, that is, in the one deposit of faith entrusted to the Church, and at the same time proposed as divinely revealed either by the solemn magisterium of the Church or by its ordinary and universal magisterium which is manifested by the common adherence of the Christian faithful under the leadership of the sacred magisterium; therefore all are bound to avoid any doctrines whatsoever contrary to them.
§2. Each and every thing which is proposed definitively by the magisterium of the Church concerning the doctrine of faith and morals, that is, each and every thing which is required to safeguard reverently and to expound faithfully the same deposit of faith, is also to be firmly embraced and retained; therefore, one who rejects those propositions which are to be held definitively is opposed to the doctrine of the Catholic Church.
Can. 751 Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Supreme Pontiff or of communion with the members of the Church subject to him.

That is to say, the Supreme Pontiff may &quot;proclaim by definitive act&quot; or an Ecumenical Council may &quot;declare (...) that a doctrine (...) is to be held definitely,&quot; or else all bishops may &quot;agree&quot; that a doctrine &quot;is to be held definitely&quot;; and such a &quot;definite&quot; doctrine must, by force of Canon 750, be believed by all, since they are required to safeguard and expound on the Deposit of the Faith — otherwise they would not be declared definitely.
Finally, Canon 751 defines heresy as a baptised Christian refusing to believe those definite teachings, which are to be believe &quot;with divine and Catholic faith.&quot; In particular, refusing to believe in the Real Presence (as the Reformed do, but not the Lutherans, who believe in Consubstantiation rather than Transubstantiation) means denying the Sacramental and saving power of Holy Communion, which is a very grave matter to Catholics as a whole.
As for the Assumption of Our Lady (the one defined in 1950 by the Apostolic Constitution Munificentissimus Deus), it was the result of the consensus of all Bishops, even though it was defined by the Holy Father. Here is the relevant passage:


And, since we were dealing with a matter of such great moment and of such importance, we considered it opportune to ask all our venerable brethren in the episcopate directly and authoritatively that each of them should make known to us his mind in a formal statement. Hence, on May 1, 1946, we gave them our letter &quot;Deiparae Virginis Mariae,&quot; a letter in which these words are contained: &quot;Do you, venerable brethren, in your outstanding wisdom and prudence, judge that the bodily Assumption of the Blessed Virgin can be proposed and defined as a dogma of faith? Do you, with your clergy and people, desire it?&quot;

But those whom &quot;the Holy Spirit has placed as bishops to rule the Church of God&quot;(4) gave an almost unanimous affirmative response to both these questions. This &quot;outstanding agreement of the Catholic prelates and the faithful,&quot;(5) affirming that the bodily Assumption of God's Mother into heaven can be defined as a dogma of faith, since it shows us the concordant teaching of the Church's ordinary doctrinal authority and the concordant faith of the Christian people which the same doctrinal authority sustains and directs, thus by itself and in an entirely certain and infallible way, manifests this privilege as a truth revealed by God and contained in that divine deposit which Christ has delivered to his Spouse to be guarded faithfully and to be taught infallibly.(6)



That is to say, the definition of the Dogma of the Assumption showcases the agreement of the Church, which by Christ's promise, has been protected from error through the action of the Holy Spirit; and denying this dogma implies necessarily that the Church can and does err and is thus not protected from error, falsifying the Christ's words in Mt 16:18, and putting in check all other doctrines which the Church holds, from the Trinity to the Resurrection to the remission of sins and salvation.