As the question states, if a creature has blindsight, do they have disadvantage on a target that is within the range of their blindsight and not otherwise hidden/covered?

The wording of the invisible condition suggests that attacks against an invisible creature have disadvantage AND the creature can't be seen without magic/special sense not BECAUSE the creature can't be seen.

Invisible Condition

An invisible creature is impossible to see without the aid of magic or a special sense. For the purposes of hiding, the creature is heavily obscured. The creature's location can be detected by any noise it makes or any tracks it leaves.

Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage.

The Special Sense Blindsense bypasses the mechanics of being Invisible

The Invisible condition states (emphasis mine):

An invisible creature is impossible to see without the aid of magic or a special sense.

Blindsight is a special type of sense, along with senses like True Sight and Tremorsense.

The condition explicitly calls out that there are special senses that bypass the condition. As Blindsight allows a creature to see the unseen, being invisible is bypassed by that sense and thus the mechanics that the Invisible condition provides are not activated.

Jeremy Crawford also provides some support:

Blindsight lets you spot an invisible creature in range, but that creature can still try to hide behind something with Stealth.

Once you can see the creature the effects of being Invisible are no longer active.

No, it doesn't have disadvantage.

A creature with blindsight can perceive its environment without using sight. Therefore it can perceive invisible creatures.

"Invisible" means "unable to be seen". The Invisible condition is actually defined that way:

An invisible creature is impossible to see without the aid of magic or a special sense.

So if someone can effectively see you, then you aren't invisible to them and the adverse effects of the Invisible condition don't apply to them. Note that there is precedent for being subject to a condition with respect to only some creatures: you are considered blinded when trying to see things that are heavily obscured.

The rules handle attacks between unseen characters in a consistent way, whether they're invisible, blind (and thus unable to see anything), or heavily obscured.

Compare Blindsight and Truesight to the rules for Faerie Fire. Creatures caught in Faerie Fire are outlined by the spell. But Faerie Fire doesn't just let you sense them, it specifies that the creature does not benefit from invisibility.

Now compare the text for blur, which gives disadvantage on attacks based on visual stimuli. An attacker is immune if it doesn't rely on sight, such as blindsight, or can see through illusions, such as truesight. It spells out that its benefits are nullified.

From a rule-based standpoint, there is some benefit that invisibility has that blur doesn't, and there's some benefit to Faerie Fire that Blindsight and Truesight lack.

From a narrative standpoint, Blindsight allows you to sense an invisible creature, but not perfectly. You may be able to sense the creature is up next to you, and maybe you might be able to work out that they are attacking. But no matter how good your ears or nose are, you wouldn't be able to track finer details like eye movement or shoulder position, so you can't be sure you know how the details of how the creature is attacking or defending.

And Truesight may have similar narrative limitations. Truesight is a way to see through illusions and invisibility, but it doesn't grant infallible vision enough to nullify these effects. While it's not spelled out WHY it doesn't fully nullify invisibility, there's a variety of explanations. The spell/item that granted it might be flawed. There might be too much information for the brain to process to see through invisibility perfectly. Because of that, there's a visual delay or motion blur or slowed reactions.

But in the end, it does come down to the DM. Me personally, I'd say the blindsight/ truesight person could use their reaction to try to perceive an oncoming attack, or bonus action to try and identify how the person is defending. Sight person would use a perception check against a stealth check from invisible person. If perception wins, I'd say the invisible person was making enough noise or shifting enough dirt or telegraphing their moves too much and they gave away their defensive stance or attack pattern, nullifying the additional benefit of invisibility.

An Invisible creature is still Invisible even if someone can see it

Invisibility is a condition that certain magical effects (e.g. Invisibility spell) gives you and the condition only ends in the way that the effect says - I don't know of any that end just because something can "see" you. While you have the condition it does what it says it does.

So, yes, an Invisible creature attacks with advantage and is attacked with disadvantage even if the target/attacker can "see" it through blindsight, tremorsense, truesight etc.

Why? Because the advantage/disadvantage comes from the Invisible condition (PHB p.291) and is distinct from the advantage/disadvantage that comes from being unseen (PHB p.195).

Does this make sense? I don't ask that question anymore.