“All you have to do is read” vs. “All you have to do is to read”

The reality of the language is such that both forms are used, on both sides of the Atlantic, but the bare-infinitive form is clearly preferred, as the stats from the Corpus of Contemporary American English (COCA) and the British National Corpus (BNC) illustrate:

                                 COCA     BNC

all you have to do is [inf]       842      72
all you have to do is to [inf]     17      20

The preference does not change if all is replaced with what, if an adverb is introduced before the infinitive, or if a different pronoun is used instead of you. However, what also does not change is that the variant with to at least exists. (A peculiar exception seem to be she and it; negation is another interesting case, but the sample size is sadly too small for those). Sometimes the ratio is a mere 1:60, but other times it's not anywhere as cut and dry. Here are all the stats I have compiled so far:

                                               COCA            BNC

all you/we/they/I have to do is [inf]      842/206/68/62    72/27/9/8
all you/we/they/I have to do is to [inf]    17/  3/ 3/ 5    20/11/4/2

all he/she/it has to do is [inf]            105/40/11         5/3/1
all he/she/it has to do is to [inf]           6/ 0/ 0         2/1/0

all you/we have to do is [adv] [inf]          9/5
all you/we have to do is to [adv] [inf]       0/0

all you/we/they/I have to do is not [inf]     1/1/1/1                 
all you/we/they/I have to do is not to [inf]  0/0/0/0     

what you have to do is [inf]                    59               8
what you have to do is to [inf]                 11               4

what you have to do is [adv] [inf]               8               1
what you have to do is to [adv] [inf]            1               0

So if you want to be on the safe side, bare infinitive certainly is the way to go. It also happens to be the more logical choice, as demonstrated by FumbleFingers in his answer. But we can't label the other option ungrammatical, and its existence can be explained logically as well, as metanalysis.

Try replacing have to with must...

2: What you must do is read a lot.

Not only does the first to disappear; the possibility of including a second one vanishes too.

I think it's easier if we assume these sentences are "cut down" versions of the [hypothetical]...

1a: All you have to do is you have to read a lot.
2a: What you must do is you must read a lot.

Then we see that OP is deleting just one half of the phrasal verb have to, which you shouldn't really do (it should be all or nothing when deleting "the verb"). But because people don't always consciously recognise have to as a "syntactic unit", they do sometimes split it as in OP's example.

It's worth pointing out that native speakers usually delete the repeated subject "you" as well, but it certainly doesn't sound seriously weird to me to leave it in (All you have to do is you read a lot.).