I don't know much about Steven Anderson, and I don't care to know much about Steven Anderson. He seems to be the successor to the Westboro cult. The media loves to showcase him to taint all Christians.
However, this does raise a question: he says homosexuals should be executed because homosexual activity was a capital offense in the Mosaic law. That can make it tricky for Bible-believing Christians to distance themselves from Anderson–or from Muslims to kill homosexuals. So what should we say about that?
i) This position is most often associated with theonomy. It's a legitimate hermeneutical issue.
ii) When Christians point out that Muslims execute homosexuals, that can be a tu quoque argument. It's responding to liberals on their own grounds. Liberals want to fine or boycott Christian businesses that refuse to cater to homosexuals weddings, boycott states that refuse to knuckle under to transgender demands regarding public restrooms, locker rooms, and intramural sports–yet they are silent on the execution of homosexuals in Muslim countries, or even do business with such countries. So it's a way of highlighting liberal duplicity.
iii) Since homosexual activity was a capital offense in the Mosaic law, Bible-believing Christians can't say that's intrinsically wrong. But what about Christian ethics? What about the new covenant?
Because ancient Israel was a nation-state, it had to have a civil and criminal law code. That would be true even if there was nothing special about Israel. As a nation-state, it had to have laws concerning violent crimes, sex crimes, and property crimes.
But over and above that, Israel had an emblematic significance. To some degree it symbolized the holiness of Yahweh. And to some degree, it prefigured the work of Christ. In addition, the purity codes made some activities sinful that are not intrinsically sinful. In the Mosaic law code, we need to distinguish between ceremonial impurity and ethical impurity.
As a result, more sins were criminalized than would be the case if Israel didn't have that emblematic significance. Indeed, in the case of the purity codes, some activities were sinful because they were criminal, rather than criminal because they were sinful.
iv) In addition, the physical presence of covenant-breakers defiled the land. The death penalty was a way of cleansing the land by eliminating offenders whose physical presence was a profanation to the cultic holiness of Eretz Israel.
Assuming that analysis is correct, under the new covenant, not as many sins are crimes. In addition, not as many crimes should carry the death penalty inasmuch as there is no longer a holy land to defile.
Although the Bible undoubtedly regards homosexual activity as intrinsically wrong, this doesn't imply that homosexual activity ought to be a felony, much less a capital offense. For the fact that it had that legal status in the Mosaic covenant may be owing to the cultic holiness of Israel. Likewise, the fact that it was a capital offense in the Mosaic law may be because execution was a way of maintaining the ritual purity of the land. In other words, a number of sins and crimes in the Mosaic law may have carried the death penalty because the physical presence of the offender desecrated the holy land. In the purity codes, ritual defilement is spread by contact. If, by contrast, the offender is executed, and his body is ritually disposed of, that action reconsecrates the land.
But the new covenant doesn't operate within that framework. That's not a part of Christian ethics.
v) If every sin was a capital offense, then everyone would be liable to summary execution. But that would have the ironic consequence of decriminalizing murder. Yet that's clearly not what Scripture intends. It's not open season on every sinner. There'd be no one left in that event.