I believe that every follower of Yeshua (aka Jesus) should be keeping God's appointed times. Passover, Shavuot, Yom Teruah, Yom Kippur, etc. I believe that doing so honors God and teaches valuable lessons.

I also believe it's important that we try to do it the way God said to as much as possible, including the timing. Of course, very few people can go to Jerusalem, and there's no altar or priesthood, so there's a lot we can't do, but we can keep the spirit of the Feasts.

We have a pretty good idea of the correct timing, though. If you believe that Yeshua is the Messiah, then you must believe that he kept the commandments correctly. We know that he kept the weekly Sabbath and the other appointed times on the same day that the Pharisees and Sadducees did. They were wrong about some things, but clearly not about everything. With a few minor exceptions, we know when the first century Jews kept the weekly Sabbath and all of the other appointed times and therefore when Yeshua kept them. They counted the months according the new moon and the weeks according to a continuous cycle of 7 days with no connection to the new moon, and so did Yeshua.

Whether you follow the sighting of the new moon or the calculated new moon, you can get the timing of the annual holy days right within a day or two, even if you've chosen the wrong method...whichever that is. Maybe you count the start of the year by the sighting of ripe barley or maybe you count it by the calculated agricultural cycles. Either method is reasonable, and I don't think we have sufficient information about first century practices.

However, if you're trying to keep the appointed times on a day that's radically different than most other people--counting the Sabbath by the new moon or calculating the months without reference to the new moon, for example--I have to wonder what makes you think you know better than Yeshua.

If you don't think keeping the feasts is important to God, this probably seems like a petty disagreement. I'll simply refer you back to the Scriptures, which plainly say that the timing of the feasts is important to him. If the King summoned you to court on Tuesday and you showed up on Wednesday because it was more convenient for you, do think he would care?

These are the appointed feasts of the LORD, which you shall proclaim as times of holy convocation, for presenting to the LORD food offerings, burnt offerings and grain offerings, sacrifices and drink offerings, each on its proper day...
Leviticus 23:37