But the article doesn't say "education on the basis of moral convictions", it says "religious and moral education on the basis of their convictions".

So generic "convictions" are protected, but only in the realm of "religious education".

Anyway, let's quote the full article for context:

Section 27 1. Everyone has the right to education.
Freedom of teaching is recognised.
2.    Education shall aim at the full development of human personality with due respect for the democratic principles of coexistence and for basic rights and freedoms.

3. The public authorities guarantee the right of parents to ensure that their children receive religious and moral instruction in accordance with their own convictions.
   
4. Elementary education is compulsory and free.
   
5. The public authorities guarantee the right of all to education, through general education programming, with the effective parti- cipation of all sectors concerned and the setting-up of educational centres.
   

6.    The right of individuals and legal entities to set up educational centres is recognised, provided they respect constitutional principles.
7.    Teachers, parents and, when appropriate, pupils shall participate in the control and management of all centres supported by the Administration out of public funds, under the terms established by the law.
8.    The public authorities shall inspect and standardise the educational system in order to ensure compliance with the laws.
9. The public authorities shall help the educational centres which meet the requirements established by the law.
10.    The autonomy of Universities is recog- nised, under the terms established by the law.

[PDF from Spain's Congress]

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa

I[f] someone tried to argue that proper science education was part of his moral convictions it probably wouldn't work.

That's interesting. Why?

(I actually agree, but you're the lawyer :-)

If you are not convinced, try it on someone who has not been entirely debauched by economics. — Piero Sraffa