I call your attention to Articles 152 and 153 of the Singaporean constitution.

Article 152 Minorities and Special Position of Malays

1) It shall be the responsibility of the Government constantly to care for the interests of the racial and religious minorities in Singapore.

2) The Government shall exercise its functions in such manner as to recognize the special position of the Malays, who are the indigenous people of Singapore, and accordingly it shall be the responsibility of the Government to protect, safeguard, support, foster and promote their political, educational, religious, economic, social and cultural interests and the Malay language.

Article 153 Muslim Religion

The Legislature shall by law make provision for regulating Muslim religious affairs and for constituting a Council to advise the President in matters relating to the Muslim religion.

Refer also to Article 15

15) Freedom of religion.
1) Every person has the right to profess and practise his religion and to
propagate it.

2) No person shall be compelled to pay any tax the proceeds of which are specially allocated in whole or in part for the purposes of a religion other than his own.

3) Every religious group has the right --

(a) to manage its own religious affairs;
(b) to establish and maintain institutions for religious or charitable purposes; and
(c) to acquire and own property and hold and administer it in accordance with law.

However, the next one is the kicker which justifies the tudung crack down:

(4) This Article does not authorise any act contrary to any general law relating to public order, public health or morality

What's with the racism streak of late? I've got far more reasons to be than you do, but at least I don't hide it behind nitpicking.