The Nazis were good at justifying stuff. Since the Fenno-Ugric peoples weren't really a threat to Germans, and didn't really live anywhere Nazi-Germany saw as "theirs", there's nothing really stopping them from elevating them racially, nor any direct conflicts as such. Now, the Nazis were often providing people with individual exceptions, literally granting "Aryaness certificates" to individuals. If your nose was straight (and I'm not using this as a joke, you literally had to send pictures) and you were important and influential they could decide you were "Aryan" regardless of your heritage. There are distinct advantages to keeping people around who can't challenge your authority provided they aren't too eyecatchingly "Jewish".

The Nazis themselves acknowledged that Germans were mixed up with lesser blood, that was ofc one of the things that lead to much misery. But built into this existed the rather pragmatic idea that you could rise above your impurity by strength of will and character and thus even a "non-pure Aryan" could be considered as one. So e.g. half- and quarter Jewish Nazi soldiers who were awarded military honours, Iron Crosses, could apply for "Germanization". All at the Fuhrers discretion of course.

Taking much of this from "Hitler's Jewish Soldiers: The Untold Story of Nazi Racial Laws and Men of Jewish Descent in the German Military", Bryan mark Rigg (2002). I have access to the (2016) Swedish edition which is somewhat updated from the English edition according to the publisher.

Now the question what Finns were was actually a question the predates the Nazis and caused a certain amount of problems in Finland itself after it was broken off from Sweden and then later on, increasingly after independence in 1917. As Kari Tarkiainen describes in "Sveriges Österland - från forntiden till Gustav Vasa" (2008). There is a sizeable (though decreasing) Swedish speaking minority in Finland that has existed there for all of recorded history. Thus a question surfaced about, when and how did these people come to Finland?

Whether you were a Swede, Finnish-Swede or Finn (in your own opinion, many Swedish speakers chose to "finnishfy" their names and "become Finns" in the so called "language battles") tended to impact whether that origin was considered ancient (i.e. earliest archaeological records), predated the arrival of Finnish speaking peoples or relative (mediaeval) newcomers conquering and subjugating the original Finns. No one really denied that ancient Germanic people had lived in Finland and left some marks, like e.g. words in the Finnish language and old placenames. Finnish has more Germanic loanwords than Estonian does, which leant credit to it. Furthermore, for some the Swedish existence in Finland would also represent a "germanisation" of Finland. A specific theory already existed that said Finns were germanic and just for some reason started speaking a foreign language, e.g. by adopting and dominating a group of non-germanic speaking people. A key difference between e.g. Japanese and Finns is that Finland can produce loads of blonde, blue-eyed "Aryans", as good as, or if not even better than Germany. Clearly proof of the inherent "Aryaness" if there ever was one.

These two streams of thought sort of coalesce in the German position. Finns are clearly to a high enough degree ennobled by an Aryan spirit, regardless of their language and whatever lesser ethnic mixing in has happened. As Finland didn't have much of a Jewish presence probably helped too. That Finland were in no way interested in ridding themselves of Jews must have come as something of a surprise to Nazi-Germany. "Finnishness" was more seen as a linguistic/cultural identity than an ethnic one, which was also the fault lines running through Finnish society existed, so the Nazi-German and Finnish ideas tended to fly past each other.

The Nazi-Germany ideology would of course been known to not entirely gel with the Finnish view of themselves. But, frankly, for most leading Finnish people war must necessitate what it must and many would be more rooted in the Swedish minority that more or less were included into the Germanic umbrella anyways. The anti-Bolshevism naturally would resonate broadly in country having been attacked by the Soviet Union and largely written off by the rest of the world. Lofty morals are for people not under existential threats. So this was a convenient peg to hang ones hat on other craziness notwithstanding.

There was no real competition in aims either. Nazi-Germany wanted large tracts of the Soviet Union and Finland wanted some parts it had lost and maybe a little more besides. Areas the Germans had little interest in anyway. The long standing German-Finnish ties also helped smooth out any ruffles. The German Empire had been instrumental in ensuring Finnish independence and many leading Finnish military officers had been trained by the Imperial German army. There exited a fairly broad cultural appreciation for Germany. Finland itself doesn't really consider itself as being of "Asian origin". If anything they are more European than any so called Indo-Europeans... That said certainly ideas like the ones Nazi-Germany held existed, the Lapua movement was vehemently anti-communist and anti-jew, likely as result of the former but was suppressed after a small scale uprising in 1932.

TL:DR Both Nazi-Germany and Finland found it useful to accept the premise that Finland was in fact Germanic for their mutual benefit in prosecuting an anti-Bolshevik war in the East. There was existing scholarly theories to fall back on and the always important fact many Finns looked "Aryan".

I can't specifically address anything vis a vis the race-laws but based on the pragmatic position and acknowledging the germanic component of Finland I would think there was no problem. If you dated a Finn well naturally it was one of the good Germanic ones. Just as an aside, somewhere close by where I live there exists a Russian stateowned property that was expropriated by the Soviet Union as war-reparations from a woman who married a German sometime before the war. So clearly the Nazi-German state could work with the concept of German-Finnish unions both nationally and personally.