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Thanks again for the civics lesson.
If I understand correctly, it was not so easy to become a naturalized citizen, but some immigrants were allowed to vote before becoming citizens and those were also subject to the military draft.

The issue which put this matter as plank #14 in the 1860 Republican platform was, iirc, a Democrat court decision which allowed a naturalized US citizen to be drafted into a foreign army, the Prussian Army, in that case.
And it makes sense from the perspective of Fugitive Slave laws -- just as slaveholders could constitutionally claw-back slaves escaped to freedom in other states, so the Democrat court ruled that foreign governments could also claw-back their citizens escaped to freedom in America.

So Republicans supported full rights for naturalized citizens, meaning no claw-backs by foreign governments.
It was the right principle and, of course, won votes among immigrant groups.

I believe resident aliens voting back in that time was pretty much the norm.

Resident aliens are subject to the draft today.

https://www.sss.gov/register/who-needs-to-register/#p1

Immigrants & Dual Nationals
With very few exceptions, all males between ages 18 and 25 must register with the Selective Service System (SSS) within 30 days of arriving in the United States. This includes U.S. born and naturalized citizens, parolees, undocumented immigrants, legal permanent residents, asylum seekers, refugees, and all males with visas of any kind which expired more than 30 days ago.
The few individuals who are exempt from this requirement are those on current non-immigrant visas, as long as they remain on a valid visa up until they turn 26. If you have received a letter from us requesting that you register, please send us copies of supporting documentation to show you are exempt.

IIRC, the issue about foreign claims on our citizens was a flashpoint for the War of 1812 following Britain taking then Americans, former Brits, and impressing them into naval service.

some immigrants were allowed to vote before becoming citizens

I had cause to revisit the old case of Minor v. Happersett (1874) and the Missouri Constitution today for another thread, and found the following:

AMENDMENTS TO THE CONSTITUTION OF 1865.
RATIFIED NOVEMBER 8, 1870.
Art. II. New sections added: Section I. Every male citizen of the United States, and every person of foreign birth who may have declared his intention to become a citizen of the United States, according to law, not less than one year nor more than five years before he offers to vote, who is over the age of twenty-one years, who has resided in this State one year next preceding his registration as a voter, and during the last sixty days of that period shall have resided in the county, city, or town where he seeks registration as a voter, who is not convicted of bribery, perjury, or other infamous crime, nor directly or indirectly interested in any bet or wager depending upon the result of the election for which said registration is made, nor serving, at the time of such registration, in the Regular Army or Navy of the United States, shall be entitled to vote at such election for all officers, State, county, or municipal, made elective by the people, or any other election, held in pursuance of the laws of this State; but he shall not vote elsewhere than in the election district where his name is registered, except as provided in the twenty-first section of the second article of the constitution. Any person who shall, after the adoption of this amendment, engage in any rebellion against this State or the United States, shall forever be disqualified from voting at any election.
. . .