Present Tense
Would it be alright if I take a rain check?
- Would it be alright if I request
[present tense] for a future opportunity [noun]?
- Would it be alright if I get
[present tense] a voucher for later [noun]?
- Would it be alright if I reschedule
[present tense] (the event) [noun]?
Would it be alright if I call you Annie?
The verb is possibly used as a present tense subjunctive, by taking the infinitive form and removing "to". (See present tense Subjunctive below)
- Would it be alright if I
were to call you Annie?
Either way, they are asking for permission to call her "Annie" from this point (in time) forward.
Past Tense
- Would it be alright if I took a rain check?
- Would it be alright if I called you Annie?
These sentences could be understood two different ways depending on context:
You are right that the speaker could be using the subjunctive mood that suggests a desire for things to be different than the currently are. (see Subjunctives below)
However, the speaker could be asking if what they did in the past was allowed or acceptable.
- Would it be alright if I took
[past tense] your car yesterday?
- Would it be alright if I called
[past tense] you Annie (in the book I wrote)?
- Would it be alright if I left
[past tense] the oven on (before I went to work)?
Subjunctives
"Are there any circumstances to allow present tense in subjunctives?"
Present Tense Subjunctives
This snippet below from gymglish.com1 has a good answer for your question about present tense subjunctives:
The present subjunctive is used in constructions such as:
They suggested that he come with them.
In English, the present subjunctive functions independently of time. It is formed by taking the infinitive form of the verb and removing "to".
Subjunctive Mood
This snippet from Wikipedia has a good explanation of what defines subjunctive mood 2.
The subjunctive is a grammatical mood, a feature of the utterance that indicates the speaker's attitude towards it. Subjunctive forms of verbs are typically used to express various states of unreality such as: wish, emotion, possibility, judgment, opinion, obligation, or action that has not yet occurred.
[1] https://www.gymglish.com/en/gymglish/english-grammar/the-subjunctive-present-tense
[2] https://en.wikipedia.org/wiki/Subjunctive_mood