Easy example : there were a great many Europeans in America during this time, including many who owned land in America. By law, they would not be eligible to vote in US Elections.

With all due respect, I'm not sure where you're sourcing this information from. For some context, let's look at the three 'Naturalization Acts' passed during the time period you cite. There's one in 1802, one in 1870, and one in 1906.

Note that states repealed land ownership as a prerequisite to the vote one by one. For example, Vermont granted universal male suffrage to citizens in its original constitution way back in 1777. But what constitutes a citizen? This was a federal issue, not a state issue, and was decided by the aforementioned series of 'Naturalization Acts', each one replacing the last.

The original text for the 1802 Naturalization Act can be found here (starting halfway down the page), with a more legible transcription available here.

For 1870, the original document is here (again, starts halfway down the page) and a typed transcription here.

For 1906, the original document is here and I can't seem to find anything more legible than that.

Anyway, none of these documents bar Europeans from somehow acquiring citizenship and from there being variably eligible to vote depending on local property restrictions. The 1802 act outlines a process where, if you're a "free white person", you announce an intent to apply for citizenship three years in advance. On the date you intend to so, if you can prove to a court that you have lived in the country for five years and in the state for at least one, as well as prove that you have "behaved as a man of good moral character", you and your family (which apparently consists of a wife and any children under twenty-one) are in. The 1870 act doesn't modify this plan in any way, but establishes harsh penalties for people who attempt to cheat this system, and expands its provisions to cover black men. The 1906 Act also keeps the spirit of the 1802 Act, but makes the process a little bit more professional and much easier to document by requiring the applicant to fill out specific paperwork rather than just announcing his relations to the court. The document has a really interesting depiction of this paperwork if you'd like to see for yourself. Furthermore, the beginning of the act establishes a federal "Bureau of Immigration and Naturalization" and grants it additional powers. However, these powers seem to be in the spirit of streamlining the process of admitting immigrants to the ranks of U.S. citizens and voters, rather than attempting to disenfranchise them. This idea is in line with the progressive ideals of Theodore Roosevelt's administration, and the Progressive Era at large.

In conclusion, a European who spoke perfect English and had been living in America for decades was overwhelmingly likely to be able to vote throughout the nineteenth century and into the twentieth. Indeed, both local and federal political parties during this period courted large immigrant voter bases, Irish and Italians being particular areas of focus.