Sequence of tense (more correctly called 'tense concord') rules do not apply here: 'ask that', in AmE and formal BrE use, governs the verb in the present subjunctive, irrespective of the tense of the verb itself.
BrE speakers, however, often substitute the preterite (simple past tense) in this sentence-position.
I agree with Philo.
The subjunctive is a complicating factor with tenses.
In the Shakespearean quotes that I dabble it it is much more common.
Thank you for your reply. It is really complicating for us, non-native speakers. We, who have to learn English from scratch, in the DIY-style, are very often full of doubts how to say or write properly, especially when our native tongue grammar is firmly embedded at the backs of our heads and is so much different from English one.
By the way, your sentence "In the Shakespearean quotes that I dabble it it is much more common." has got two pronouns 'it' following each other and I have to admitt that I don't remember if I've come across such a construction. So, does it mean that the first 'it' is an object of the transitive verb 'to dabble' and the second 'it' is a dummy subject of the clause "...it it is much more common."?