Luther also advocated for the state to burn down Jewish synagogues didn't he?
Yes, Martin Luther argued for this very thing in
On the Jews and their lies. Here is the relevant extract:
In Deuteronomy 13 [:12 ff.] Moses writes that any city that is given to idolatry shall be totally destroyed by fire, and nothing of it shall be preserved.
If he were alive today, he would be the first to set fire to the synagogues and houses of the Jews. For in Deuteronomy 4 [:2] and 12 [:32] he commanded very explicitly that nothing is to be added to or subtracted from his law. And Samuel says in 1 Samuel 15 [:23] that disobedience to God is idolatry. Now the Jews’ doctrine at present is nothing but additions of the rabbis and the idolatry of disobedience, so that Moses has become entirely unknown among them (as we said before), just as the Bible became unknown under the papacy in our day.
So also, for Moses’ sake, their schools cannot be tolerated; they defame him just as much as they do us. It is not necessary that they have their own free churches for such idolatry.
Second,
I advise that their houses also be razed and destroyed. For they pursue in them the same aims as in their synagogues. Instead they might be lodged under a roof or in a barn, like the gypsies. This will bring them home to them the fact that they are not masters in our country, as they boast, but that they are living in exile and in captivity, as they incessantly rail and lament about us before God.
Third, I advise that all their prayer books and Talmudic writings, in which such idolatry, lies, cursing, and blasphemy are taught, be taken from them.
Fourth, I advise that their rabbis be forbidden to teach henceforth on pain of loss of life and limb. For they have justly forfeited the right to such an office by holding the poor Jews captive with the saying of Moses (Deuteronomy 17 [:10 ff]) in which he commands them to obey their teachers on penalty of death, although Moses clearly adds: “what they teach you in accord with the Law of the Lord.” Those villains ignore that. They wantonly employ the poor people’s obedience contrary to the Law of the Lord and infuse them with this poison cursing and blasphemy.
Martin Luther,
On the Jews and Their Lies in Franklin Sherman (ed.),
Luther’s Works: The Christian in Society IV (55 vols, Philadelphia, 1971), xlvii, 269.