I answered this in the past:
In your context of trying to find a partner, I would not consider anything as red flag yet.

I'd rather think it's more towards the relationship status of one side vs the other, not so much the gender.

If both are single, then there's nothing to go "wrong" because no one's cheating on anyone. Congratulations!
If one is single and the other isn't, there is a higher chance that something would go wrong because one side is still searching and is more likely to "cross the other's line".
If both are not single, then I believe it is harder for something to go wrong, but when it does, it's a 4-side explosion.
In all cases, there's no point to discuss if the person in question oversteps his/her boundaries so I'm speaking for generally responsible adults. In a committed relationship, both have the responsibility to ensure nothing goes wrong... E.g.
- if your other half is insecure then avoid 1:1 with opposite gender or "report in" more often.
- if can't hold your drink then don't drink lah

If your partner's insecurity feels suffocating to you, that means there's misalignment on expectations and you need to talk it out, or else it's the end lah. This is one of the "values" to evaluate during dating stage, because some people's expectations may not be something you want to comply with (read: don't stick your d in crazies).