Yes, Constitution of India is a perfect blind of rigidity and flexibility. More than 100 Constitutional amendment since its inception is testimony to that. It is neither too rigid as that of US constitution and nor that flexible as that of British.
The Provisions of the constitution can be changed by different kinds of majority such as 2/3rd of the present and voting plus absolute majority. This kind of majority is not that difficult for a government of absolute majority to obtain. But at the same time it is difficult to pass a CAA for a minority government.
Further the provisions of the constitution amendment act has to pass the basic structure test initiated by Supreme court in Keshvanand bharti case. The middle path of blend is taken so that constitution remain dynamic as per the demand of present and future and the sanctity of the basic values remain intact.