Anti-immigration sentiment is (generally) not a question of 'values' per-se but one of tribalism. Natives are seen as one tribe and Muslims/Africans etc. are another, and if the other tribe takes over in sufficient numbers they will use their power to disadvantage the native white European population. It's not that values in themselves need protecting but that there is a 'clash of civilisations' between the civilisation of Europe and the civilisation of brown migrants which can only end in the subjection of one to the other.
Obviously, I'm not of the opinion that other races should not be allowed to live in Europe, but they should only be allowed to come legally if they can contribute, and they must leave any backwards thinking (religion>secularism) behind (if they have any such opinions).
Illegals are much more likely to commit a crime (than natives or legal migrants) and will draw benefits for years before they pay anything back into the system, and this is not disputable or to be argued against, it is simply a fact.
There are many more reasons, but it's late, so I might be back tomorrow.