TLDR
Get sunder on supp every game, and you really want sunder in solo, but if you are ok losing your first couple buffs you can do without it. (Yes it's getting nerfed, still get it, the level 1 and level 10+ value is too good)
If you have sunder and they don't poke around the jg looking for an invade but don't get caught out and killed quickly.
If both you and your opponent have sunder, just farm like normal unless you have an absurdly good matchup
If your supp is invading, just farm like mad, don't try to help them, if they get rotated on by 3 people and killed but you farmed, it's a win.
Sunder Note: The level 10 spike in dmg from 625 to 1000 is really big for securing that first objective. Pay attention when you have it and try to take the weighted coin toss on the objective
Doing a Support side Invade
Check 1: have sunder Check 2: either have an insane early game 1v1 (less likely with the change for health pots and chalice to no longer stack) or they don't have sunder Check 3: ADC is able to clear purple and survive a 2v1 in lane
If both of these are true go ahead and invade speed. If no one is around, just clear the camp and go back to lane. If they contest you want to play careful, the more time you buy the better. Denying farm is more important than actually getting farm in this scenario. If they try to ignore you and clear the camp, hit them with your abillities and the camp with sunder.
There are extra layers if the enemy supp is also invading speed
You do not necessarily need to invade if all these things are true, but you can
Dealing with a Support side invade
If the supp is caught in your JG early enough (before minions spawn) you should be able to collapse on them and kill them. Just try to be back to your own camp for when it spawns.
If the supp is invading speed then try to avoid bailing the JG out once the camps are close to spawning. As JG you want to farm the best you can despite the invade. They can only sunder 1 camp, so sacrificing your speed in order to get the rest of the JG camps is going to be the best plan. If you happen to have a better 1v1 into the supp that is invading you can try to take the 1v1 before farming. Another option if you spot the supp invading before the camp spawns but too late to kill them, abandon the speed buff to farm other camps.
If you are in a 5 stack and aren't happy with this method of dealing with an invade there are strategies to deal with it using all 5, but you can discuss and experiment amongst yourselves.
If you don't go sunder in supp you are leaving yourself open to a purple invade as well, in that case play it slow with your abillities till you would be securing the camp, this way if the supp walks up you can turn on them and kill them for the attempt. The natural 2v1 makes this more viable, but you will want both of your abillities to be up for it to be effective. This will lessen your pressure in lane as your abillities won't be up for clear, but it's the price you pay for not going sunder in supp.
Doing a solo side invade
If doing an invade you will need sunder.
If you don't win the 1v1 going for an invade is going to be risky regardless, this is because you can lose pressure wave 1 and lose your own blue in response. This can be fixed by having the JG start at blue, then go red, backs, speed, but you are still risking dying.
There are generally 2 schools of thought for the timing of when you show up for the invade. Either you show up as soon as possible to get info and decide if you want to bail on the invade, or you show up at the last second to sunder the camp and walk to lane. Each have their own risks and rewards.
If you are against a god that really doesn't want sunder (glass cannon solos like susano or anubis for example) it will be generally better to do the last second invade because they won't be able to get help in time, and if they go sunder to match your secure they are going to suffer later in the game so you can give up a little pressure for a few waves.
If you are against a god who is fine w/ sunder (most "traditional" tankier solos) then you can instead opt to show up earlier, and take a quick trade (remember to bail out if they bring help). Then if you are forced to take a reset, either bc they disengage or you do, you can press tab to check their relic, if they don't have sunder you can look to repeat with a last second invade.
Dealing with a solo invade
If you have sunder, just worry about out trading them before it spawns and then coin toss the buff.
If you have someone else local they can come chase off a solo who is showing up early.
If they show up at the last minute you can try to use the fact you have a relic they don't to win a trade wave 1 and counter invade the blue. Warning, they will hit 2 before you if given equal clear wave 1
Otherwise try to weather the storm. If you are really on time for your blue buff respawn you can potentially clear the second spawn before they get there, but otherwise it will be near impossible to out secure buffs. You can try to have your JG there for blue respawn to take a 2v1 or better speed clear before they can contest, but if it's a 2v2 you have to look for a fight taking the fact you have essentially an extra PVP relic as an advantage, but if that isn't enough to tip the scales in your favor you are just going to be losing the buff.