For your starting class, I would recommend Barbarian. You'll get a bit more health than the druid, and you'll also get better saving throw proficiencies, skill proficiencies, and armor proficiencies.

To elaborate on saving throws, Barbarian gets STR and CON proficiencies, while Druid gets INT and WIS. Generally you want to prioritize saving throws which will protect you from instant-disabling effects; things that will immediately take you out of the fight. CON and WIS are probably the most important in this regard. CON is the most common save in the game. It covers poison damage and the poison status effect, but more importantly, stun, paralyze, petrification, death, blindness, life drain, and long-term diseases and curses. WIS covers fear, charm, and mind control.

If both these saves are important, then why do I say the Barbarian's saves are better? Because STR saves are far, far, far more common than INT saves. STR saves come into play from a variety of enemies, usually for resisting prone, grapple, and knockback, which will be important for a meat shield. INT saves, on the other hand, are extremely rare, only used by a tiny select few monsters, mainly mind-flayers and their kin. Therefore, while CON and WIS are roughly equal priority, STR will give you much more benefit than INT.

Regardless which you choose, it would be a good idea to take the Resilient feat for whichever of CON and WIS you don't get proficiency in. This may impact your leveling order if you feel you desperately need this feat, but probably shouldn't make too much of a difference early on.

As far as the starting proficiencies go, Barbarians give you all martial weapon proficiencies, while druid is more limited. Armor proficiencies are the same, although druids cannot use metal. This may be a significant caveat for this multiclass combo if your DM chooses to enforce it.

For skill proficiencies, the Barbarian skill options relevant to you are Athletics, Intimidation, and Perception. Athletics makes you better at resisting grapples, which is very important for a tank. Intimidation might be a good option if your DM lets you use it in combat, and lets you use STR for it rather than CHA. Perception helps with group perception checks to keep your group from getting surprised. For Druid skill proficiencies, Perception is really the only skill relevant to a tank. There isn't much in the Druid skill list that's important for your optimization goal.

As for continuing progression, you'll want at least three levels of Barbarian for Bear totem resistance to all damage. If tankiness is your only goal, then the feat/attribute boost at 4th level Barbarian is tempting, but there isn't much else in the way of defense available in the next few levels. At most I'd say to max out Barbarian at level 5 in order to pick up the Extra Attack and +10 movement while not wearing heavy armor. After that, you'd probably be better off going druid.

CONCLUSION: Take one level in Barbarian to start. From here you can either go Druid 2 for Wild Shape, or continue on to Druid 4 to get your attribute boost/Feat as soon as possible. After that, return to Barbarian and continue to Barbarian level 3 or 5, depending on how much you want the extra feat, extra attack, and movement bonus. Once you're satisfied with Barbarian, max out Druid.

The multiclass prerequisites, in my opinion, are best treated as suggestions rather than requirements. They do not serve any balance function—they serve primarily to help prevent players from falling into the trap of taking a class that their ability scores will not support. The reciprocal nature of the requirements, in my opinion, have more to do with making things symmetric and minimizing the degree to which the order you take classes matters than it does to do with anything concerned with balance.

As such, I have never stopped a player who knew what they were doing from doing any multiclassing they liked. This has caused zero problems, and I see no way that it could. The worst case scenario, as far as I can tell, is Paladin/Warlock using the Hexblade patron, which can now be done without needing Strength 13, which is quite desirable for this combination since Strength does little for them thanks to Hex Warrior. However, Hexblade is widely considered to be an anomaly in its own right, which means it would be quite sad indeed to limit everyone else for the sake of this one case. For me, even this combination has not caused any real problems. There is certainly nothing about a Dexterity-based Barbarian/Fighter that is going to cause more problems.