Getting a new infraction for expired tabs does not generally disqualify a person for a deferred finding on an earlier speeding ticket. However, some courts have their own specific idea as to who qualifies for a deferral. Additionally, using the deferral for the speeding ticket (a moving violation) will usually not stop a person from deferring a tabs violation (a non-moving violation). A person can generally do one of each every seven years. The more important questions are should a person use his or her deferral in these situations? A deferral is generally not a preferred result. An experienced attorney should be able to give some other, and maybe better, alternatives after reviewing the specifics of each case.
Legally, this new ticket does not disqualify you from a deferred on the previous ticket. However, a deferred is within the judge's discretion, so the judge may say no.
You cannot ask for a deferred on both tickets. Asking for a deferred on the expired tabs ticket gets you nowhere anyway, because as you noted, it is a nonmoving violation.