There is a discussion in 'Eruvin, Daf 6b-7a about whether or not we can take the stringencies of two conflicting opinions. The Gemara seems adamant that we cannot, though there are examples brought that seem to contradict this. I've tried to follow the trail of Tosafoth and other Gemaras that are referenced, but they have not led me to any conclusion. Furthermore, there is nothing in the margin notes ('Ein Mishpat, Ner Mitzvah) that I see that is relevant to guide one to a conclusion. The Gemara seems to finally conclude that, so long as the two different opinions don't directly contradict, and therefore cannot coexist, you can take the stringencies of the two opinions.
First, if the two conflicting opinions are irreconcilable and mutually exclusive, of course you cannot take the two conflicting stringencies. What is this Gemara teaching us?
Second, despite the above, there is a widely-practiced ruling among Ashkenazim to have a Mezuzah angled, so as to satisfy the two conflicting opinions, one that it should be vertical, and the other that it should be horizontal. Since this appears to actually satisfy neither opinion, the Vilna Gaon is known to have objected, and those who follow him post the Mezuzah vertically, to satisfy the primary opinion. Is this ruling in the Gemara here in 'Eruvin the basis for this ruling of the GR"A, and if so, how did it come about that so many people follow the practice to fulfill the conflicting opinions?