There is a mixed message about Blood Magic in the games. On the one hand it is taught by demons and spirits and can be used to actively deal with spirits and demons, for summoning, for complex spells, for any spell, etc. Also, in the lore, unlike normal magic which draws on Fade energy (mana) for its power (that's why normal magic weakens the veil and why demons can find mages easier than non mages when they dream, because mages are naturally a bridge between the two worlds), blood magic is supposed to be purely physical, and we are told some magical orders only practiced Blood Magic (see the wiki) because it did not involve the Fade in any way and so was supposed to be "safer" than dealing with the Fade all the time to cast spells (using mana). It really is unclear if the entities of the fade must be dealt with to cast Blood Magic, because on the one hand that theory is supported, and on the other we are told mana is a fade connection, where as blood has it's own inherent powers.
Look at the Darkspawn. They get their magic from the Taint, which is basically their life-blood. It grants them an endless energy supply, and Avernus described the power of the Taint as alien to the Fade. Also, to achieve this Tainted state, an unprecedented blood ritual was apparently conducted by the Magisters to enter the Black City, which is like the center of the fade, but the least fadey part of the Fade because no Fade creature ever goes there, and it is nigh impossible to enter the Black City. So, even in the role of the Taint-as-not-Fade-Magic, it is confusing because of the role of the Black City in the Taint story.
Anyway. Point is. Yes: if all blood magic involves dealing with fade entities to work, then the Fade Tears in DA:I would logically make it so demons are less willing to help mages cast these spells because they can simply waltz over to the nearest Fade Tear and enter the mortal world. No: if blood is really the opposite of mana and draws power not from the Fade, then blood magic should still be the same, besides maybe a few demons no longer teaching it because they're busy with the Fade Tears, and maybe a few demons being less interested in hijacking mages in general because they're already frolicking around Thedas.