We shouldn't grant anyone entry as an immigrant if they do not share our vision of democratic values and swear an oath saying so. Not even one should be allowed who won't. I understand that the oath of citizenship was changed recently to remove the "defend the United States". Don't know if that was true, but if so, says a lot to me about those managing immigration, and none of it good.
You’re thinking all people think like democratic people. Clearly, this is not the case with children. But, even with people who have reached the age of majority, it is a rare person who thinks like a free person who hasn’t been cultured to be a free person. But, some people think being free means, for example, being able to vote to redistribute the wealth, as opposed to being responsible to support oneself and one’s family. Recall Lincoln’s adage, to the fox and to the sheep, freedom means different things. To people of the right, freedom means being self-responsible, and to people of the left, it means being freed from self-responsibility.
Possibly you mean to say that only people who can demonstrate a sufficient understanding of what it means to be a free person, as in a written or oral test, can be allowed in. The old way was to have such a test (as imperfect as any test is), after a period of residency in conjunction with a citizenship test. This way, we would see whether the person was able to behave as a free person such as by obeying the law and supporting himself and his family, in addition to being able to demonstrate some knowledge concerning being a citizen of a free society.
Your sense is correct that the other side wants to bring in refugees, put them on welfare, and give them the right to vote. Those people would be cultured to think that freedom means voting to redistribute the wealth.