A child should always get all intervention they require to make them successful regardless of the eligibility category. If the primary disability is SLD, they should still receive goals, services, and/or accommodations for anxiety if the evaluations show they are needed to access the general education curriculum. If the primary disability is OHI, they should still receive goals, services, and/or accommodations for SLD if the evaluations show they are needed to access the general education curriculum. Your child's life should not be ruined either way because they school district is required to provide needed interventions in all areas of need.
Having said that, I feel the primary disability is important, because that tends to be how the teachers view the child. Do you want the teachers to think your child's anxiety is the bigger problem or the reading comprehension. Also, what do you as a parent feel is affecting your child the most - the anxiety or the reading comprehension? But it will also depend on what the evaluations say, and it sounds like the school district may argue that the data points to OHI -but make them PROVE that if you disagree.
I'm also very suspect when school districts want to avoid the SLD classification. They may feel that this holds them to a higher standard, such as providing evidence-based multisensory structured instruction, even though my thought is this is required even if SLD is a secondary category. There also might be state laws that kick in regarding SLD's that they're trying to avoid.
Go with your gut - you know you child the best. But also be prepared to back up your decision by referencing data in the evaluations and (if you think it will be helpful) asking the general education teacher what s/he feels is your child's bigger obstacle.