If your child's dyslexia is remediated to the point that they don't need anything except maybe extra time on tests, then such a school might work, but if they need anything more, you need to focus on schools that are known to be open to students with learning disabilities. Almost every (non-religious) school around here will be welcoming of LGBTQ students, but much less open to kids with learning disabilities.
This. I say this is a veteran DC private school parent who is close with families with kids who really struggled to find a good fit for their queer kids who had learning differences (2 x dyslexia, 1 x dyscalculia, 1 x multiple diagnoses).
We all went to a K-8 that everybody knows is super supportive of LGBTQ+ kids; that piece was all good. Then, these kids went on to Field, Burke, APS, and MCPS (not all @ 9th).
Field experience was an academic disaster but fortunately this family could easily afford to pay for essentially an LD 'governess' who was at their house 5 days a week to manage the academic piece. (social experience was very good for kid)
Burke experience was fine -- that kid still had multiple tutors but kid was able to access a "normal"curriculum on a ... slow-average track. Social part = excellent.
MCPS was the best academically, from outsider's perspective. That kid basically got 1:1 intensive, tailored instruction on the public's dime. Social piece seemed ok, but, this kid had challenges that were distinct from kid's queer identity.
APS, good for this kid with mild LD. VERY hard social transition for this kid. VERY. I think especially after growing up in such a nurturing school environment. This kid's family has an enormous social circle of supportive LGBTQ+ people so that was helpful (camps, clubs, family members) but apparently their APS HS was so hard.
This is obviously anecdotal and my cisgender kids do not have learning differences. I thought I'd post to give you anecdata to help you form your own investigations.