Whether consent would be required for repeal of the Human Rights Act (HRA) depends both on law and on an important aspect of the devolution settlement known as the Sewel Convention.
The UK Parliament at Westminster is sovereign and may legislate anything it wishes for the devolved nations. The Scottish Parliament may not repeal or amend the Human Rights Act 1998 (HRA). This is the combined effect of the Scotland Act 1998 s29(2)(c) and Schedule 4.
The Scottish Parliament, when operating within its legislative competence, may not enact anything that is incompatible with any of the Convention rights - Scotland Act 1998 s29
Scottish Ministers do not have power to make any subordinate legislation, or to do any other act, so far as the legislation or act is incompatible with any of the Convention rights - (see Scotland Act 1998 s.57).
The term "convention rights" is defined in the Act (s.126) as having the same meaning as in the Human Rights Act 1998 (HRA).
The Scottish Parliament is not prevented completely from legislating in relation to human rights. For example, it created the Scottish Human Rights Commission. However, the Scottish Parliament is prevented from amending the HRA and is also prevented from legislating incompatibly with the convention rights as included in the Human Rights Act 1998. In this way, the law has embedded human rights into the Scottish devolution settlement. It may reasonably be claimed that human rights lie at the heart of that settlement.
This is NOT a law but a convention that Westminster would seek the consent of the Scottish Parliament before legislating:
Would repeal (by Westminster) of the HRA engage the Sewel Convention?
Dr Mark Elliott has undertaken a detailed analysis of this question on his Public Law for Everyone blog. – Could the devolved nations block repeal of the Human Rights Act and the enactment of a new Bill of Rights?
Elliot argues that the repeal of the Human Rights Act (“HRA”) by itself, without anything more, such as its replacement by a British Bill of Rights or the withdrawal of the UK from the ECHR, would not trigger the Sewel Convention
An alternative argument is to be found at the UK Constitutional Law Association: HRA Watch: Reform, Repeal, Replace? Iain Jamieson: The repeal of the HRA and the Sewel Convention in Scotland
(Note: A response to the Jamieson argument was been published by Mark Elliott - Public Law for Everyone - The Scottish Parliament, the Sewel Convention and Repeal of the Human Rights Act: a postscript)
Whether it would be politically sensible for Westminster to repeal (without Scottish consent) the HRA in relation to Scotland is an entirely different matter. It would be highly likely to turn Scottish opinion much more in favour of independence.
As Iain Jamieson argues, repeal of the HRA would necessitate amendment of the Scotland Act in which "convention rights" are currently defined as being the rights within the HRA. However this point is detailed point is handled (and several legislative ways seem possible) an alteration of the relative powers of Westminster and Edinburgh seems inevitable and that would amount to a quite fundamental alteration to the devolution settlement.
If Jamieson is right, and I submit that his view is to be preferred, then the Sewel Convention would be engaged and Sturgeon has made it quite clear that consent would not be likely. The Elliott view also indicates that the Sewel Convention could be engaged if Westminster were to go beyond mere repeal of the HRA.
All of this would leave it for Westminster to risk the political consequences and exercise its sovereign powers to amend the Scotland Act or, alternatively, back off and leave things alone in Scotland.
Deeper political problems seem to exist in relation to Northern Ireland where the European Convention on Human Rights was part of the Good Friday Agreement which is, itself, an international agreement.
Whether it would be desirable for the level of human rights protection to vary from one part of the United Kingdom to another is a difficult question on which further in depth consideration may come to be needed. That is a matter for another day.